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HP 33s Owner's Manual

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RPN/ALG Scientific Calculator
File name 33s-E-Manual-1008-Publication(1st).doc
Printed Date : 2003/10/8
HP 33s
Owner's Manual
H
HP Part No. F2216-90020
Printed in China
Edition 1
Size : 13.7 x 21.2 cm
Page : 386

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Table of Contents

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   Summary of Contents for HP 33s

  • Page 1   HP 33s RPN/ALG Scientific Calculator Owner’s Manual HP Part No. F2216-90020 Printed in China Edition 1 File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 2 Hewlett–Packard Co. is also prohibited. 4995, Murphy Canyon Rd, Suite 301 San Diego, CA 92123 Printing History Edition 1 November 2003 File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 3: Table Of Contents

    Range of Numbers and OVERFLOW ......1–16 Doing Arithmetic .............1–16 One–Number Functions..........1–17 Two–Number Functions ..........1–17 Controlling the Display Format ..........1–18 Periods and Commas in Numbers ........1–18 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 4 Chain Calculations in RPN mode ........2–10 Work from the Parentheses Out ........2–10 Exercises..............2–12 Order of Calculation ..........2–13 More Exercises ............2–14 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 5 Hyperbolic Functions............4–6 Percentage Functions............4–6 Physics Constants ..............4–8 Conversion Functions ............4–9 Coordinate Conversions ..........4–10 Time Conversions ............4–12 Angle Conversions.............4–13 Unit conversions ............4–13 Probability Functions............4–14 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 6 Variables in Equations ..........6–4 Numbers in Equations ..........6–5 Functions in Equations..........6–5 Parentheses in Equations ..........6–6 Displaying and Selecting Equations ........6–6 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 7 Accuracy of Integration ............8–5 Specifying Accuracy ............8–6 Interpreting Accuracy ...........8–6 For More Information ............8–8 Operations with Complex Numbers The Complex Stack............9–1 Complex Operations ............9–2 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 8 The Statistics Registers in Calculator Memory ....11–12 Access to the Statistics Registers ........ 11–12 Programming Part 2. Simple Programming Designing a Program ............12–3 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 9 The Catalog of Programs (MEM)........ 12–20 Clearing One or More Programs ....... 12–21 The Checksum............12–21 Nonprogrammable Functions .......... 12–22 Programming with BASE..........12–22 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 10 Using SOLVE in Program..........14–5 Integrating a Program............14–7 Using Integration in a Program ........14–10 Restrictions on Solving and Integrating ......14–11 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 11 The Self–Test..............A–5 Warranty ................ A–6 Service ................A–7 Regulatory information ............A–9 User Memory and the Stack Managing Calculator Memory ..........B–1 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 12 How SOLVE Finds a Root ........... D–1 Interpreting Results ............D–2 When SOLVE Cannot Find a Root ........D–8 Round–Off Error ............. D–14 Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 13 How the Integral Is Evaluated..........E–1 Conditions That Could Cause Incorrect Results ....... E–2 Conditions That Prolong Calculation Time ......E–7 Messages Operation Index Index Contents File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 15: Part 1. Basic Operation

    Part 1 Basic Operation File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 17: Getting Started

    Display contrast depends on lighting, viewing angle, and the contrast setting. To Å Ù Ã increase or decrease the contrast, hold down the key and press 1–1 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 18: Highlights Of The Keyboard And Display

    ) before pressing the key for the desired function. For example, to turn the º Å calculator off, press and release the shift key, then press 1–2 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 19: Alpha Keys

    One of the first things you need to know is how to clear: how to correct numbers, clear the display, or start over. 1–3 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 20 Clears the displayed number to zero or cancels the current situation (such as a menu, a message, a prompt, a catalog, or Equation–entry or Program–entry mode). 1–4 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 21 If you are viewing a completed equation, the equation is deleted with no verification. 1–5 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 22: Cursor Keys

    Using Menus There is a lot more power to the HP 33s than what you see on the keyboard. This is because 14 of the keys are menu keys. There are 14 menus in all, which provide many more functions, or more options for more functions.
  • Page 23 HP 33s Menus Menu Menu Chapter Name Description Numeric Functions  ˆ  ˆ L.R.    Linear regression: curve fitting and linear estimation.     Arithmetic mean of statistical x– and y–values; weighted mean of statistical x–values.
  • Page 24 HP 33s Menus (continued) Menu Menu C h a p t e r N a m e Description Other functio ns 1, 3, 12   Memory status (bytes of memory available); catalog of variables; catalog of programs (program labels).
  • Page 25: Exiting Menus

    Keys: Display:  _    Þ       ¹ ¡    Å  1–9 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 26: Rpn And Alg Keys

    In RPN mode and algebraic mode, the results of all calculations are listed. However, in RPN mode only the results are listed, not the calculations. 1–10 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 27: The Display And Annunciators

    The symbols on the display, shown in the above figure, are called annunciators. Each one has a special significance when it appears in the display. 1–11 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 28 HP 33s Annunciators Annunciator Meaning Chapter á á The " (Busy)" annunciator blinks while an operation, equation, or program is executing. ¹ When in Fraction–display mode (press É ), only one of the " " or " " halves of the "...
  • Page 29 HP 33s Annunciators (continued) Annunciator Meaning Chapter Ö Õ When the keys are active to 1, 6 scroll the display, i.e. there are more digits to the left and right. º Î to see the rest of a decimal number; use the left and right–cursor keys Ö...
  • Page 30: Keying In Numbers

    Rounds number to fit the display  format. Ï .000042 Automatically uses scientific notation    because otherwise no significant digits would appear. 1–14 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 31: Understanding Digit Entry

    Keys: Display: Description:  _ Digit entry not terminated: the number 1–15 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 32: Range Of Numbers And Overflow

    All calculations can be simplified into one–number functions and/or two–number functions. 1–16 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 33: One-number Functions

    3. Key in the second number. (Do not press 4. Press the function key. (For a shifted function, press the appropriate shift key first.) 1–17 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 34: Controlling The Display Format

    For example, the number one million looks like:  if you press {  } or  if you press {  }. 1–18 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 35: Number Of Decimal Places

    SCI 4 display mode. The "5" following the "E" is the exponent of 10: 1.2346 × 10 1–19 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 36: Showi N G Fu Ll 12-digit Precisio N

    For example, in the number 14.8745632019, you see only "14.8746" when the display mode is set to FIX 4, but the last six digits ("632019") are present internally in the calculator. 1–20 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 37: Fractions

    Î release Fractions The HP 33s allows you to type in and display fractions, and to perform math operations on them. Fractions are real numbers of the form. a b/c where a, b, and c are integers; 0 ≤ b ≤ c; and the denominator (c) must be in the range 2 through 4095.
  • Page 38: Displaying Fractions

    (FIX 4). Displaying Fractions ¹ É Press to switch between Fraction–display mode and the current decimal display mode. 1–22 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 39: Messages

    Binary mode). All displayed messages are explained in appendix F, "Messages." Calculator Memory The HP 33s has 31K bytes of memory in which you can store any combination of data (variables, equations, or program lines). 1–23 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc...
  • Page 40: Checking Available Memory

     {  } {  }, which safeguards against the unintentional clearing of memory. 2. Press {  } (yes). 1–24 Getting Started File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 41: Rpn: The Automatic Memory Stack

    What the Stack Is Automatic storage of intermediate results is the reason that the HP 33s easily processes complex calculations, and does so without parentheses. The key to automatic storage is the automatic, RPN memory stack.
  • Page 42: The X And Y-registers Are In The Display

    "rolling" the contents downward, one register at a time. You can see each number when it enters the X–register. 2–2 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 43: Exchanging The X- And Y-registers In The Stack

    Y–register. For example, converts rectangular coordinates in the X– and Y–registers into polar coordinates in the X– and Y–registers. 2–3 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 44: Arithmetic - How The Stack Does It

    Z–register, and that the former contents of the T–register are lost. You can see, therefore, that the stack's memory is limited to four numbers. 2–4 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 45: How Enter Works

    You can use the replicating feature of to other advantages. To add a Ï Ù number to itself, press 2–5 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 46: How Clear X Works

    Å cancels program entry. During digit entry, backspaces over the displayed number. 2–6 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 47: The Last X Register

    See appendix B for a comprehensive list of the functions that save x in the LAST X register. 2–7 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 48: Correcting Mistakes With Last X

    Suppose you made a mistake while calculating 16 × 19 = 304 There are three kinds of mistakes you could have made: 2–8 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 49: Reusing Numbers With Last X

    96.704 Y 96.704 96.704 96.704 52.3 947 52.3947 149.0987 LAST X 52.3947 149.0987 2.8457 52.3947 LAST X 52.3947 52.3947 2–9 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 50: Chain Calculations In Rpn Mode

    If you were working out this problem on paper, you would first calculate the intermediate result of (12 + 3) ... 2–10 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 51 (12 + 3) = 1 5 … then you would multiply the intermediate result by 7: (15) × 7 = 105 Solve the problem in the same way on the HP 33s, starting inside the parentheses: Keys: Display: Description: Ï...
  • Page 52: Exercises

    (5 + 6). Finally, you would multiply the two intermediate results to get the answer. Work through the problem the same way with the HP 33s, except that you don't have to write down intermediate answers—the calculator remembers them for you.
  • Page 53: Order Of Calculation

    (or results) will be needed at one time (the stack can hold no more than four numbers). 2–13 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 54: More Exercises

    Ï ¸ Ï w à ¯ ? 12.5 Ï ¸ Ï Ï ) à ¯ ? 12.5 Calculate: 2–14 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 55 Ã ¸ ¯ Ï 8.33 7.46 0.32 3.15 Ã ¸ Ï ¸ Ã ¯ ? 2.75 1.71 2.01 2–15 RPN: The Automatic Memory Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 57: Storing Data Into Variables

    Storing Data into Variables The HP 33s has 31K bytes of user memory: memory that you can use to store numbers, equations, and program lines. Numbers are stored in locations called variables, each named with a letter from A through Z. (You can choose the letter to remind you of what is stored there, such as B for bank balance and C for the speed of light.)
  • Page 58: Storing And Recalling Numbers

    Clears the number in the display.   _  Prompts for variable. Copies Avogadro's numbers from    A the display. 3–2 Storing Data into Variables File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 59: Viewing A Variable Without Recalling It

    . (If it is a binary number with more than 12 digits, use the Ö Õ keys to see the rest.) 3–3 Storing Data into Variables File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 60: Clearing Variables

    X–register and does not affect the stack. New value of variable = Previous value of variable {+, –, ×, ÷} x. 3–4 Storing Data into Variables File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 61: Recall Arithmetic

    Suppose the variables D, E, and F contain the values 1, 2, and 3. Use storage arithmetic to add 1 to each of those variables. 3–5 Storing Data into Variables File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 62: Exchanging X With Any Variable

    Display: Description:  Stores 12 in variable A.  _ Displays x. º v  Exchanges contents of the 3–6 Storing Data into Variables File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 63: The Variable "i

    (i) function. This is a programming technique called indirect addressing that is covered under "Indirectly Addressing variables and labels" in chapter 13. 3–7 Storing Data into Variables File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 65: Real-number Functions

    Exponential and Logarithmic Functions Put the number in the display, then execute the function — there is no need to press Ï 4–1 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 66: Quotient And Remainder Division

    To calculate the cube root of a number x, key in x and press ¹ ! To calculate a power x of 10, key in x and press 4–2 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 67: Trigonometry

    Note that the calculator cannot exactly represent π, since π is an irrational number. 4–3 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 68: Setting The Angular Mode

    For example, the calculated –13 sin π (radians) is not zero but –2.0676 × 10 , a very small number close to zero. 4–4 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 69 θ by a rectangular to polar conversion, which converts (x,y) to (r,θ). See "Coordinate Conversions" later in this chapter. 4–5 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 70: Hyperbolic Functions

    Display: Description: Þ {  } 2 Rounds display to two decimal  places. Ï 15.76  Calculates 6% tax.  4–6 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 71 The order of the two numbers is important for the %CHG function. Note The order affects whether the percentage change is considered positive or negative. 4–7 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 72: Physics Constants

    –928.476362×10 –26 –1 {  } Neutron magnetic moment – 0.96623640×10 –26 –1 {  } Muon magnetic moment – 4.49044813×10 4–8 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 73: Conversion Functions

    Conversion Functions There are four types of conversions: coordinate (polar/rectangular), angular (degrees/radians), time (decimal/minutes–seconds), and unit (cm/in, °C/°F, l/gal, Kg/lb). 4–9 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 74: Coordinate Conversions

    3. The resulting display (the X–register) shows either r (polar result) or x θ (rectangular result). Press to see or y. y, x θ θ r y, x θ 4–10 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 75 , in degrees. When the values are converted to rectangular coordinates, the x–value yields R, in ohms; the y–value yields X , in ohms. 4–11 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 76: Time Conversions

    {  } 6  Sets FIX 6 display format. Ë Ë   _  1/7 as a decimal fraction. 4–12 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 77: Angle Conversions

    1. Key in the angle (in decimal degrees or radians) that you want to convert. º µ ¹ ´ 2. Press . The result is displayed. Unit conversions The HP 33s has eight unit–conversion functions on the keyboard: ºC, ºF, gal. To Convert: Press: Displayed Results: ¹...
  • Page 78: Probability Functions

    It passes the spectral test of D. Knuth, Seminumerical Algorithms, vol. 2, London: Addison Wesley, 1981.) 4–14 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 79 X–register. ¯ Divides combinations of  women by total combinations to find probability that any one combination would have all women. 4–15 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 80: Parts Of Numbers

    (The internal number is represented by 12 digits.) Refer to chapter 5 for the behavior of RND in Fraction–display mode. 4–16 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 81: Names Of Functions

     . "SIN" is the name of the function as it will appear in program lines (and usually in equations also). 4–17 Real–Number Functions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 83: Fractions

    Enters 1   ¹ É Displays x as a decimal number.  ¹ É Displays x as a fraction.   5–1 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 84: Fractions In The Display

    These are examples of entered values and the resulting displays. For comparison, the internal 12–digit values are also shown. The annunciators in the last column are explained below. 5–2 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 85: Accuracy Indicators

    "a little above" the displayed numerator, and means the exact numerator is "a little below". 0 7/16 0 7/16 0 7/16 (0.40625) (0.43750) (0.46875) 5–3 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 86: Longer Fractions

    Shows all decimal digits..  Stores value in A. º È  Views A..  Å Å  Clears x. 5–4 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 87: Changing The Fraction Display

    (/c value is 4095). This is the default fraction format. 5–5 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 88: Examples Of Fraction Displays

    Examples of Fraction Displays The following table shows how the number 2.77 is displayed in the three fraction formats for two /c values. 5–6 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 89 Enters the starting value.   Ë Ë Ã Subtracts the change.      Finds the 85–percent value to the nearest 5–7 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 90: Rounding Fractions

    The cumulative round off error. º · {  } 8   Clears flag 8. ¹ É  Turns off Fraction–display mode. 5–8 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 91: Fractions In Equations

    7, 8, and 9. Setting flag 7 turns on Fraction–display mode — ¹ É isn't programmable. See "Flags" in chapter 13. See chapters 12 and 13 for information about working with programs. 5–9 Fractions File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 93: Entering And Evaluating Equations

    Entering and Evaluating Equations How You Can Use Equations You can use equations on the HP 33s in several ways: For specifying an equation to evaluate (this chapter). For specifying an equation to solve for unknown values (chapter 7). For specifying a function to integrate (chapter 8).
  • Page 94 L. ¥ Stores L; calculates V in cubic  inches and stores the result in V.  6–2 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 95: Summary Of Equation Operations

    (bytes of memory). Å Leaves Equation mode. You can also use equations in programs — this is discussed in chapter 12. 6–3 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 96: Entering Equations Into The Equation List

    , the A..Z annunciator shows that you can press a variable key to enter its name in the equation. 6–4 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 97: Numbers In Equations

    The cursor changes back when you press a nonnumeric key. Functions in Equations You can enter many HP 33s functions in an equation. A complete list is given under “Equation Functions” later in this chapter. Appendix G, "Operation Index,"...
  • Page 98: Parentheses In Equations

    . This activates Equation mode and turns on the EQN annunciator. The display shows an entry from the equation list: 6–6 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 99: Editing And Clearing Equations

    You can edit or clear an equation that you're typing. You can also edit or clear equations saved in the equation list. 6–7 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 100    . Example: Editing an Equation. Remove 25 in the equation from the previous example. 6–8 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 101: Types Of Equations

    Å Leaves Equation mode.  Types of Equations The HP 33s works with three types of equations: Equalities. The equation contains an "=", and the left side contains more than just a single variable. For example, x is an equality.
  • Page 102 "=" in an equation essentially treated as "_". The value is a measure of how well the equation balances. Ï The HP 33s has two keys for evaluating equations: . Their actions differ only in how they evaluate assignment equations: returns the value of the equation, regardless of the type equation.
  • Page 103: Using Enter For Evaluation

    Stores L in millimeters;  ¸ ¥  calculates V in cubic millimeters, stores the result  in V, and displays V. 6–11 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 104: Using Xeq For Evaluation

    The prompt gives the variable name and its current value, such as  . ¥ To leave the number unchanged, just press 6–12 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 105: The Syntax Of Equations

    Operator Precedence Operators in an equation are processed in a certain order that makes the evaluation logical and predictable: 6–13 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 106 (1 – f) must be entered as  , with the "  " operator inserted between P and the left parenthesis. 6–14 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 107: Equation Functions

    "subtraction" ( ). For a number, use à For a variable, use parentheses and . These are valid equations: 6–15 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 108 Perimeter = a + b + h ( θ φ φ θ The following equation obeys the syntax rules for HP 33s equations: 6–16 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8...
  • Page 109 ¸ h ¸ n º j ¯ h º | ¯ k º j ¯ h º | Ï 6–17 Entering and Evaluating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 110: Syntax Errors

    (See "Editing and Clearing Equations" earlier in this chapter.) By not checking equation syntax until evaluation, the HP 33s lets you create "equations" that might actually be messages. This is especially useful in programs, as described in chapter 12.
  • Page 111: Solving Equations

    X to solve for x. The equation then prompts for a value for every other variable in the equation. 3. For each prompt, enter the desired value: 7–1 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 112 Starts the equation. ¸ h Ù  ¸ h ¸ h    _  Ï  Terminates the equation 7–2 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 113 ¥  Retains 0 in V; prompts  for G. ¥  Retains 9.8 in G; solves  for T.  7–3 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 114 R. ¥ .0821 Stores .0821 in R;  value  prompts for T. Ï Ù 273.1 Calculates T (Kelvins).   7–4 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 115: Understanding And Controlling Solve

    Through successive iterations, SOLVE finds a value for the unknown that makes the value of the equation equal to zero. 7–5 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 116: Verifying The Result

    If the X– and Y–register values are close together, and the Z–register value is close to zero, the estimate from the X–register may be an approximation to a root. 7–6 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 117: Interrupting A Solve Calculation

    T and solved for D. The value that was left in T was a good (realistic) one, so it was used as a guess when solving for T . 7–7 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 118 V= ( 40 – H ) × ( 20 – H ) × 4 × H 7–8 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 119 — by looking at the value of the previous estimate of the root (in the Y–register) and the value of the equation at the root (in the Z–register). 7–9 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 120 The plot of the value of this equation looks like this. 7500 _ (40 _ ) (20 _ ) 4 20,000 _ 10 _ 10,000 7–10 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 121: For More Information

    SOLVE works, how to interpret results, what happens when no solution is found, and conditions that can cause incorrect results. 7–11 Solving Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 123: Integrating Equations

    ∫ a specified variable (  d_). The function may have more than one variable. " works only with real numbers. 8–1 Integrating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 124: Integrating Equations ( ∫ Fn)

    Example: Bessel Function. The Bessel function of the first kind of order 0 can be expressed as π ∫ cos( π 8–2 Integrating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 125  ∫ calculates result for  π ∫  ) (t º j ¯ The final result for J (2).  8–3 Integrating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 126 8–4 Integrating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 127: Accuracy Of Integration

    E. 8–5 Integrating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 128: Specifying Accuracy

    Rolls down the limits of    integration from the Z–and T–registers into the X–and Y–registers. º d Displays the current Equation.  8–6 Integrating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 129 1/100 as large as the uncertainty of the SCI 2 result calculated previously. Þ {  } 4 Restores FIX 4 format.    8–7 Integrating Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 130: For More Information

    For More Information This chapter gives you instructions for using integration in the HP 33s over a wide range of applications. Appendix E contains more detailed information about how the algorithm for integration works, conditions that could cause incorrect results, conditions that prolong calculation time, and obtaining the current approximation to an integral.
  • Page 131: Operations With Complex Numbers

    Ï 2. Press 3. Type the real part. Complex numbers in the HP 33s are handled by entering each part (imaginary and real) of a complex number as a separate entry. To enter two complex numbers, ¹ c you enter four separate numbers. To do a complex operation, press before the operator.
  • Page 132: Complex Operations

    1. Enter the complex number z, composed of x + i y, by keying in y 2. Select the complex function. 9–2 Operations with Complex Numbers File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 133 Here are some examples of trigonometry and arithmetic with complex numbers: Evaluate sin (2 + i 3) Keys: Display: Description: Ï Result is 9.1545 – i  9–3 Operations with Complex Numbers File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 134 Completes entry of second  number and then multiplies  the two complex numbers. Result is 11.7333 – i 3.8667. 9–4 Operations with Complex Numbers File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 135: Using Complex Numbers In Polar Notation

    Many applications use real numbers in polar form or polar notation. These forms use pairs of numbers, as do complex numbers, so you can do arithmetic with these numbers by using the complex operations. Since the HP 33s's complex operations work on numbers in rectangular form, convert polar form to rectangular form º...
  • Page 136 ¹ c Ù Adds L  ¹ ° Converts vector back to  polar form; displays r, θ  9–6 Operations with Complex Numbers File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 137: Base Conversions And Arithmetic

     Converts just the integer part {  } (125) of the decimal number to base 16 and displays this value. 10–1 Base Conversions and Arithmetic File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 138: Arithmetic In Bases 2, 8, And 16

    If a number has a fractional part, only the integer part is used for an arithmetic calculation. The result of an operation is always an integer (any fractional portion is truncated). 10–2 Base Conversions and Arithmetic File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 139 ¹ ¶ {  }  Result in hexadecimal base. ¹ ¶ {  }  Restores decimal base. 10–3 Base Conversions and Arithmetic File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 140: The Representation Of Numbers

    1. ¹ ¶ {  }  Negative decimal number. 10–4 Base Conversions and Arithmetic File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 141: Range Of Numbers

    Each 12–digit display of a long number is called a window. 36 - bit number Highest window Lowest window (displayed) 10–5 Base Conversions and Arithmetic File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 142 ( ) to view the obscured window. Press to displayed Press to displayed left window right window 10–6 Base Conversions and Arithmetic File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 143: Statistical Operations

    Statistical Operations The statistics menus in the HP 33s provide functions to statistically analyze a set of one– or two–variable data: Mean, sample and population standard deviations. y ˆ x ˆ Linear regression and linear estimation ( Weighted mean (x weighted by y).
  • Page 144: Entering One-variable Data

    Even if only one value of an x, y–pair is incorrect, you must delete and reenter both values. To correct statistical data: 11–2 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 145 Ï Reenters the first data pair.   There is still a total of two data pairs in the statistics registers. 11–3 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 146: Statistical Calculations

    She randomly picks six people, observes each one as he or she carries out the process, and records the time required (in minutes): 11–4 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 147 º (     Calculates the mean      price weighted for the  quantity purchased. 11–5 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 148: Sample Standard Deviation

    {σ  } for the population standard deviation of the x–values. º + Press {σ  } for the population standard deviation of the y–values. 11–6 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 149: Linear Regression

    {  } Slope of the calculated line. {  } y–intercept of the calculated line. 11–7 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 150 ¹ ¡ {  } Clears all, previous statistical  data. Ï 4.63 Enters data; displays n.   Ï 5.78 11–8 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 151 What if 70 kg of nitrogen fertilizer were applied to the rice field ? Predict the grain yield based on the above statistics. 11–9 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 152: Limitations On Precision Of Data

    11–10 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 153: Summation Values And The Statistics Registers

    Views Σy ×  register.    × Views Σx    register.  × Views Σy register.  11–11 Statistical Operations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 154: The Statistics Registers In Calculator Memory

    Refer to "Managing Calculator Memory" in appendix B. Access to the Statistics Registers The statistics register assignments in the HP 33s are shown in the following table. Statistics Registers Register...
  • Page 155: Part 2. Programming

    Part 2 Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 157: Simple Programming

    Rather than repeat the given keystrokes each time (varying only the "5" for the different radii), you can put the repeatable keystrokes into a program: 12–1 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 158 The answer!  We will continue using the above program for the area of a circle to illustrate programming concepts and methods. 12–2 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 159: Designing A Program

    However, adjacent programs need a label between them to keep them distinct. Program Returns Programs and subroutines should end with a return instruction. The keystrokes are: º Ô 12–3 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 160: Using Rpn, Alg And Equations In Programs

    For input, you can prompt for a variable with the INPUT instruction, you can get an equation to prompt for its variables, or you can take values entered in advance onto the stack. 12–4 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 161: Entering A Program

    5. End the program with a return instruction, which sets the program pointer back º Ô to   after the program runs. Press Å ¹ £ 6. Press ) to cancel program entry. 12–5 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 162: Keys That Clear

    This fuller name appears briefly in the display whenever you execute a function — as long as you hold down the key, the name is displayed. 12–6 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 163 Å Å Cancels program entry (PRGM annunciator off). A different checksum means the program was not entered exactly as given here. 12–7 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 164 º Î  Checksum and length of equation.  Å Å  Cancels program entry. 12–8 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 165: Running A Program

    1. As for regular execution, make sure program entry is not active (PRGM annunciator off). 12–9 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 166 (release)  π Ø (hold)   (release)  Ø (hold)   End of program. Result is correct. (release)  12–10 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 167: Entering And Displaying Data

    "R" is the variable's name, " ? " is the prompt for information, and 0.0000 is the current value stored in the variable. 12–11 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 168 12–12 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 169: Using View For Displaying Data

    This is a display only, and does not copy the number to the X–register. If Fraction–display mode is active, the value is displayed as a fraction. Ï Pressing copies this number to the X–register. 12–13 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 170: Using Equations To Display Messages

    You can then use Ö to scroll the display. If you don't want the program to stop, see "Displaying Information without Stopping" below. 12–14 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 171 Stores the surface area in S.    º · {  } Sets flag 10 to display  Ë equations.    12–15 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 172 Prompts for H. ¥    Message displayed. ¥  Volume in cm  ¥  Surface area in cm  12–16 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 173: Displaying Information Without Stopping

    VIEW instruction or an equation that's displayed (flag 10 set), the variable or equation is displayed instead — and the display remains after the 1–second pause. 12–17 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 174: Interrupting A Running Program

    . The pointer then moves to the preceding line. (If you are deleting more than one consecutive program line, start with the last line in the group.) 12–18 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 175: Program Memory

    While program entry is active, there are three ways to change the program pointer (the displayed line): 12–19 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 176: Memory Usage

    Delete specific programs. (Press while the label is displayed.) º See the checksum associated with a given program segment. (Press Î 12–20 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 177: Clearing One Or More Programs

    3. Press and hold to display  checksum and  length. For example, to see the checksum for the current program (the "cylinder" program): 12–21 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 178: Nonprogrammable Functions

    In addition, each equation in a program has a checksum. See "To enter an equation in a program line" earlier in this chapter. Nonprogrammable Functions The following functions of the HP 33s are not programmable: ¹ ¡ ¹ r Ë Ë...
  • Page 179: Selecting A Base Mode In A Program

    "D" in Hexadecimal mode. Decimal mode set: Hexadecimal mode set: PRGM PRGM     PRGM PRGM     12–23 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 180: Polynomial Expressions And Horner's Method

    Fills the stack with x.    Ï   Ï   Ï     ¸     12–24 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 181 A more general form of this program for any equation (((Ax + B)× + C)× + D)× + E would be: 12–25 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 182                  Checksum and length: 8926 57 12–26 Simple Programming File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 183: Programming Techniques

    A routine typically starts with a label (LBL) and ends with an instruction that alters or stops program execution, such as RTN, GTO, or STOP, or perhaps another label. 13–1 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 184: Calling Subroutines (xeq, Rtn)

          Starts D again.  1 Starts subroutine.    Returns to routines D.   13–2 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 185: Nested Subroutines

    (a nested subroutine), labeled Q, to do the repetitive squaring and addition. This saves memory by keeping the program shorter than it would be without the subroutine. 13–3 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 186: Branching (gto)

    Unconditional branching uses the GTO (go to) instruction to branch to a program label. It is not possible to branch to a specific line number during a program. 13–4 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 187: A Programmed Gto Instruction

    ¹ r You can use to move the program pointer to a specified label or line number without starting program execution. 13–5 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 188: Conditional Instructions

    There are three categories of conditional instructions: Comparison tests. These compare the X–and Y–registers, or the X–register and zero. 13–6 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 189: Tests Of Comparison (x?y, X?0)

     . Example: The "Normal and Inverse–Normal Distributions" program in chapter 16 uses the x<y ? conditional in routine T: 13–7 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 190: Flags

    Meanings of Flags The HP 33s has 12 flags, numbered 0 through 11. All flags can be set, cleared, and tested from the keyboard or by a program instruction. The default state of all 12 flags is clear.
  • Page 191 VIEW statement: 1. Program execution halts. 2. The program pointer moves to the next program line. 13–9 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 192 5 through 11. These statuses of these flags can be determined by executing the FS ? instruction from the keyboard. (See "Using Flags" below.) 13–10 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 193 X– and Y–inputs for a Straight–line model curve. Line L0003 sets flag 0 so that line W0007 takes the natural log of the X–input for a Logarithmic–model curve. 13–11 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 194 Note that lines S0003, S0004, L0004, and E0003 clear flags 0 and 1 to ensure that they will be set only as required for the four curve models. 13–12 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 195 If flag 1 is set ...    ... takes the natural log of the Y–input.   .  13–13 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 196 Ï 3. Press to insert the message in the current program line and end Equation–entry mode. 13–14 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 197 Displays message, then shows the fraction.        Goes to beginning of program.    Checksum and length: 34AA 120 13–15 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 198: Loops

    This is called looping.                13–16 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 199: Conditional Loops (gto)

    For example, the following routine uses a loop to diminish a value A by a constant amount B until the resulting A is less than or equal to B. 13–17 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 200: Loops With Counters (dse, Isg)

    These functions accomplish the same thing as a FOR–NEXT loop in BASIC:  variable = initial–value  final–value  increment  variable 13–18 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 201 > program line if this ccccccc fff. 13–19 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 202         º È Press Z to see that the loop–control number is now 11.0100.  13–20 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 203: Indirectly Addressing Variables And Labels

    ISG i ∫ STO +,–, × ,÷ i FN d i x < > i RCL +,–, × ,÷ i SOLVE i 13–21 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 204: The Indirect Address, (i)

    The functions listed below can use (i) as an address. For GTO, XEQ, and FN=, (i) refers to a label; for all other functions (i) refers to a variable or register. 13–22 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 205: Program Control With (i)

    Line Y0003 calls the subroutine to compute   x ˆ and line Y0008 calls a different subroutine to compute after i has been increased by 6: 13–23 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 206 The next routine is L, a loop to collect all 12 known values for a 3 × 3 coefficient matrix (variables A – I ) and the three constants ( J – L ) for the equations. 13–24 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 207: Equations With (i)

     means variable i. The following program uses an equation to find the sum of the squares of variables A through Z. 13–25 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 208       Branches for next variable.   Ends program. Checksum and length of program: E005 23 13–26 Programming Techniques File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 209: Solving And Integrating Programs

    1. Begin the program with a label. This label identifies the function that you want SOLVE to evaluate (  label). 14–1 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 210 R = The universal gas constant (0.0821 liter–atm/mole–K or 8.314 J/mole–K). T = Temperature (kelvins; K = °C + 273.1). 14–2 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 211 SOLVE evaluates to find the value of the unknown variable. Û Selects P; prompts for V.  value  14–3 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 212 º Ô Ends the program.   Å  Cancels Program–entry mode. Checksum and length of program: 36FF 21 14–4 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 213: Using Solve In Program

    X–register) before executing the SOLVE variable instruction. The two instructions for solving an equation for an unknown variable appear in programs  label  variable 14–5 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 214 The following excerpt is from a program that allows you to solve for x or y by pressing X or Y. 14–6 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 215: Integrating A Program

    To integrate a programmed function: 1. Enter a program that defines the integrand's function. (See "To write a ∫ program for FN" below.) 14–7 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 216 If you want the equation to prompt for variable values instead of including INPUT instructions, make sure flag 11 is set. 14–8 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 217 Integrates function from 0 to 2;  ∫ displays result.   Ý {  } Restores Degrees mode.  14–9 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 218: Using Integration In A Program

    Specifies the function.    ∫ Integrates the normal function using the dummy variable D.     14–10 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 219: Restrictions On Solving And Integrating

    (Refer to "Nested Subroutines" in chapter 13.) ∫ The SOLVE and FN operations automatically set Decimal display format. 14–11 Solving and Integrating Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 221: Mathematics Programs

    X = R sin(P) cos(T) Y = R sin(P) sin(T) T = arctan (Y/X) Z = R cos(P) P = arctan 15–1 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 222 =U i + V j + W k The vector displayed by the input routines (LBL P and LBL R) is V 15–2 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 223 Displays or accepts input of P.           θ  Calculates R cos(P) and R sin(P). 15–3 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 224 Loops back for polar conversion and display/input.    Checksum and length: CE3C 33 Defines beginning of vector–addition routine.       15–4 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 225    Calculates (ZU – WX), which is the Y component.            15–5 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 226        θ Calculates the magnitude of the U, V, W vector.      15–6 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 227 Add vectors by pressing b. Subtract vector one from vector two by pressing c. Compute the cross product by pressing 15–7 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 228 North, 7.3 kilometers East and 0.76 kilometers below. Use the rectangular to polar conversion capability to find the total distance and the direction to the transmitter. 15–8 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 229 ? What is the angle between the resultant of the force vectors and the lever ? 15–9 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 230 Sets P equal to 74.   Adds the vectors and displays the  resultant R. ¥  Displays T of resultant vector.  15–10 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 231 Display: Description: (In RPN mode) Starts polar input routine.   ¥ Defines the radius as one unit  vector.  15–11 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 232: Solutions Of Simultaneous Equations

          Specifics regarding the inversion process are given in the comments for the inversion routine, I. 15–12 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 233   Calculates F' × determinant = CD – AF.             15–13 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 234             Calculates D' × determinant = FG – DI.   15–14 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 235 Sets index value to point, to last clement in first row.      Sets index value to point to last element in second   15–15 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 236 Returns to the calling program.   Checksum and length: 7F00 24 This routine calculates the determinant.       15–16 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 237 (A × F × H) – (D × B × I).   Returns to the calling program or to   . Checksum and length: 7957 75 Flags Used: None. 15–17 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 238 23X + 15Y + 17Z = 31 8X + 11Y – 6Z = 17 4X + 15Y + 12Z = 14 15–18 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 239 Displays next value.   ¥ Displays next value.   ¥ Displays next value.   ¥ Displays next value.   15–19 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 240: Polynomial Root Finder

    To solve a fourth–order polynomial, it is first necessary to solve the resolvant cubic polynomial: y + b where b = – a – 4a 15–20 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 241 ≥ 0, the roots are real; if d < 0, the roots are If the discriminant d = (a – a ± − ± − complex, being 15–21 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 242 Checksum and length: 2582 21 Starts solver setup routine.    Stores location of coefficients to use.    15–22 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 243      Calculates – a /2 –       Calculates – a /2 + 15–23 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 244       Calculates a    Stores a    Displays real root of fifth–order polynomial. 15–24 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 245 Solves for remaining roots of cubic and stores roots.    Gets real root of cubic.    Stores real root. 15–25 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 246       JK – a   Use 1 if JK – a /2 = 0   15–26 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 247    root. Were there any complex roots ?    Displays complex roots if any.    15–27 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 248 0, then 0 is a real root. Reduce the polynomial by one order by factoring out The order and the coefficients are not preserved by the program. 15–28 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 249 The order of the polynomial is same as the number of roots you get. 8. For a new polynomial, go to step 3. 15–29 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 250 ¥  Displays the third root.  ¥  Displays the fourth root.  ¥  Displays the fifth root.  15–30 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 251 ¥ Displays the imaginary part of the  fourth root.  The third and fourth roots are –1.00 ± 1.00 i. 15–31 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 252: Coordinate Transformations

    = u cos – v sin θ θ y = u sin + v cos The HP 33s complex and polar–to–rectangular functions make these computations straightforward. 15–32 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8...
  • Page 253 Old coordinate system [0, 0] θ m, n New coordinate system 15–33 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 254    This routine converts from the new system to the old system. Prompts for and stores U.    15–34 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 255 6. To translate from the old system to the new system, continue with step 7. To translate from the new system to the old system, skip to step 12. 15–35 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 256 (X, Y) system, to points in the (X', Y') system. Convert point P' which is in the (X',Y') system, to the (X,Y) system. 15–36 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 257 Stores –9 in X. value  ¥  Stores 7 in Y and calculates U.  ¥  Calculates V.  15–37 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 258  Stores 2.7 in U.  z ¥  Stores –3.6 in V and calculates  ¥  Calculates Y.  15–38 Mathematics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 259: Statistics Programs

    . (For definitions of these values, see "Linear Regression" in chapter 11.) Samples of the curves and the relevant equations are shown below. The internal regression functions of the HP 33s are used to compute the regression coefficients. 16–1 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc...
  • Page 260 Data values of large magnitude but relatively small differences can incur problems of precision, as can data values of greatly different magnitudes. Refer to "Limitations in Precision of Data" in chapter 11. 16–2 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 261 Defines common entry point for all models. Clears the statistics registers.      Stores the index value in i for indirect addressing. 16–3 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 262 Calculates the coefficient b.   If flag 1 is seta takes the natural antilog of b.        16–4 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 263 Returns to the calling routine.   Checksum and length: 65AB 18 y ˆ    This subroutine calculates for the logarithmic model. 16–5 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 264   Checksum and length: CC13 21 y ˆ This subroutine calculates for the power model.       16–6 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 265 E for an exponential curve; or P for a power curve. ¥ 3. Key in x–value and press ¥ 4. Key in y–value and press 16–7 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 266 Also, estimate y for an x value of 37. Estimate x for a y value of 101. 16–8 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 267 Enters correct x–value of data  pair.  ¥ Enters y–value of data pair.   ¥ 36.2 Enters x–value of data pair.   16–9 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 268 You will need to reenter the data values each time you run the program for a different curve fit. 16–10 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 269: Normal And Inverse-normal Distributions

    σ π This program uses the built–in integration feature of the HP 33s to integrate the equation of the normal frequency curve. The inverse is obtained using Newton's method to iteratively search for a value of x which yields the given probability Q(x).
  • Page 270       Calculates the derivative at X guess      Calculates the correction for X guess 16–12 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 271 This subroutine calculates the integrand for the normal    − − ÷ ÷ function       16–13 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 272 . (If the standard deviation is 1, just press 5. To calculate X given Q(X), skip to step 9 of these instructions. 16–14 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 273  ¥ Accepts the default value of zero for   ¥ Accepts the default value of 1 for S.  16–15 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 274 20 percent of the students would have failed to achieve ? Keys: Display: Description: (In RPN mode)  Starts the initialization routine.  16–16 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 275: Grouped Standard Deviation

    This program allows you to input data, correct entries, and calculate the standard deviation and weighted mean of the grouped data. 16–17 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 276   Increments (or decrements) N.       Displays current number of data pairs.    16–18 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 277 –value (data point) and press ¥ 4. Key in f –value (frequency) and press ¥ 5. Press after VIEWing the number of points entered. 16–19 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 278 Enter the following data and calculate the grouped standard deviation. Group Keys: Display: Description: (In RPN mode)  Prompts for the first x value  16–20 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 279 Prompts for the fourth x   ¥ Prompts for the fourth f   ¥ Displays the counter.   16–21 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 280 (sx) of the six data points. ¥ Calculates and displays   weighted mean ( Å  Clears VIEW. 16–22 Statistics Programs File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 281: Miscellaneous Programs And Equations

    Note that any problem can be viewed from two perspectives. The lender and the borrower view the same problem with reversed signs. 17–1 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 282 SOLVE calculation ( I ). The order in which you're prompted for values depends upon the variable you're solving for. 17–2 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 283 10.5% annual interest compounded monthly. The purchase price of the car is $7,250. Your down payment is $1,500. 17–3 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 284 The answer is negative since the loan has been viewed from the borrower's perspective. Money received by the borrower (the beginning balance) is positive, while money paid out is negative. 17–4 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 285 (In RPN mode) º d  Displays leftmost part of the TVM equation. Û  Selects F; prompts for P.  17–5 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 286: Prime Number Generator

    This process continues until a prime number is found. 17–6 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 287 LB L X P D → F P [ / ] x = 0? √ D > P + 2 → 17–7 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 288 Tests to see whether all possible factors have been tried.    If all factors have been tried, branches to the display 17–8 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 289 (In RPN mode) Calculates next prime number   after 789. ¥ Calculates next prime number   after 797. 17–9 Miscellaneous Programs and Equations File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 291: Part 3. Appendixes And Reference

    Part 3 Appendixes and Reference File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 293: Support, Batteries, And Service

    A: Exponent of ten; that is, 2.51 × 10 Q: The calculator has displayed the message   . What should I do ? A–1 Support, Batteries, and Service File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 294: Environmental Limits

    If the battery annunciator is on, and the display dims, you may lose data. If data is lost, the   message is displayed. A–2 Support, Batteries, and Service File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 295 Remove one of the two batteries once. Press down the holder. Push the plate to the shown direction and lift it. Plate Holder A–3 Support, Batteries, and Service File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 296: Testing Calculator Operation

    1. Do the self–test described in the next section. If the calculator fails the self test, it requires service. A–4 Support, Batteries, and Service File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 297: The Self-test

    You can halt this factory test by pressing any key. A–5 Support, Batteries, and Service File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 298: Warranty

    Replacement products may be either new or like-new. 2. HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase, for the period specified above, due to defects in material and workmanship when properly installed and used.
  • Page 299: Service

    The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. Nothing herein should be construed as constituting an additional warranty. HP shall not be liable for technical and editorial errors or omissions contained herein.
  • Page 300 Chile 800-360999 Columbia 9-800-114726 Peru 0-800-10111 Central America & Caribbean 1-800-711-2884 Guatemala 1-800-999-5105 Puerto Rico 1-877-232-0589 Costa Rica 0-800-011-0524 A–8 Support, Batteries, and Service File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 301: Regulatory Information

    ROTC = Rest of the country Regulatory information This section contains information that shows how the HP 33s scientific calculator complies with regulations in certain regions. Any modifications to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the 33s in these regions.
  • Page 302 Japan この装置は、情報処理装置等電波障害自主規制協議会(VCCI)の基準 に基づく第二情報技術装置です。この装置は、家庭環境で使用することを目的 としていますが、この装置がラジオやテレビジョン受信機に近接して使用され ると、受信障害を引き起こすことがあります。 取扱説明書に従って正しい取り扱いをしてください。 Noise Declaration. In the operator position under normal operation (per ISO 7779): LpA<70dB. A–10 Support, Batteries, and Service File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 303: User Memory And The Stack

    How to clear (purge) all of user memory and reset the system defaults, and Which operations affect stack lift. Managing Calculator Memory The HP 33s has 31K bytes of user memory available to you for any combination of ∫ stored data (variables, equations, or program lines). SOLVE, FN, and statistical ∫...
  • Page 304: Resetting The Calculator

    B–2 User Memory and the Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 305: Clearing Memory

    . (You will be pressing three keys simultaneously). When you release all three keys, the display shows   if the operation is successful. B–3 User Memory and the Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 306: The Status Of Stack Lift

    X–register. (Refer to chapter 2, "The Automatic Memory Stack.") All functions except those in the following two lists will enable stack lift. B–4 User Memory and the Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 307: Disabling Operations

    Including all operations performed while the catalog is displayed except Ï {  } and {  } , which enable stack lift. B–5 User Memory and the Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 308: The Status Of The Last X Register

    The former stores x in LAST X; the latter stores the recalled number in LAST X. B–6 User Memory and the Stack File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 309: Alg: Summary

    CMPLX, RND, RAND, IP, FP, INTG, SGN, ABS, e , unit conversion. and y 4. nPr, nCr, %CHG. 5. ×, ÷, INT÷, Rmdr. 6. +, –. C–1 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 310: Doing Two-number Arithmetic In Alg

    Power Functions In ALG mode, to calculate a number y raised to a power x, key in y x, then Ï press C–2 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page: 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 311: Percentage Calculations

    Suppose that the $15.76 item cost $16.12 last year. What is the percentage change from last year's price to this year's ? C–3 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 312: Permutation And Combination

    To display the quotient and remainder produced by 58 ÷ 9 Keys: Display: Description: ¹ b Ï  Displays the quotient.  º ` Ï  Displays the remainder.  C–4 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page: 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 313: Parentheses Calculations

    Ï ¸ ¯ Ï ¯ Ï In the second case, the key acts like the key by displaying the result of C–5 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 314: Reviewing The Stack

    RPN mode. You can press Ö < º ; ) to review each registers. C–6 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page: 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 315: Coordinate Conversions

    Ý {  }  Sets Degrees mode. º ±   Calculates x.  Ø   Displays y.  C–7 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 316: Integrating An Equation

    Enter the complex number z. (Use parentheses for z if the real part exists). Select the complex function. Ï Press to calculate. C–8 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page: 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 317 = 4 – i 3 Keys: Display: Description: º y Ù  Real part of result. ¹ c º |  C–9 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 318: Arithmetic In Bases 2, 8, And 16

    + E9A Keys: Display: Description: ¹ ¶ {  } Sets base 16; HEX  annunciator on. Ù Ï Result.   C–10 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page: 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 319: Entering Statistical Two-variable Data

    4. The display shows n, the number of statistical data pairs you have accumulated. 5. Continue entering x, y–pairs. n is updated with each entry. C–11 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 320   Reenters the first data pair.   There is still a total of two data pairs in the statistics registers. C–12 ALG: Summary File name 33s-E-Manual-1008-Publication(1st).doc Page: 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 321: More About Solving

    If f(x) has one or more local minima or minima, each occurs singly between adjacent roots off f(x) (figure d, below). D–1 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 322: Interpreting Results

    (12–digit) precision. Interpreting Results The SOLVE operation will produce a solution under either of the following conditions: D–2 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 323 Enter the equation as an expression: Keys: Display: Description: º d Select Equation mode.  z ¸  Enters the equation.  Ù ¸  D–3 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 324 Ù Enters the equation.  Ã Ï  º Î  Checksum and length.  Å  Cancels Equation mode. D–4 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 325 If the pole occurs at a value of x that is exactly represented with 12 digits, then that value would cause the calculation to halt with an error message. D–5 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 326 Description: Your initial guesses for   _  the root. º d Selects Equation mode;  displays the equation. D–6 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 327  Å  Cancels Equation mode. Now, solve to find the root. Keys: Display: Description: Your initial guesses for  D–7 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 328: When Solve Cannot Find A Root

    The search is concentrated in a local "flat" region of the function (see figure c, below). The ending value of f(x) is the value of the function in this region. D–8 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 329 – 6x + 13 = 0. It has a minimum at x = 3. Enter the equation as an expression: D–9 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 330 Enter the equation as an expression. Keys: Display: Description: º d  Selects Equation mode. Ã , h Enters the equation.  D–10 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 331 It's apparent from inspecting the equation that if x is a negative number, the smallest that f(x) can be is 10. f(x) approaches 10 as x becomes a negative number of large magnitude. D–11 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 332 Keys: Display: Description:   _  º d  Selects Equation mode; displays the left end of the equation. D–12 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 333 Solve for X using initial guesses of 10 and –10 Keys: Display: Description: Enters guesses.   _    D–13 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 334: Round-off Error

    Underflow occurs when the magnitude of a number is smaller than the calculator can represent, so it substitutes zero. This can affect SOLVE results. For example, consider the equation D–14 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 335 Because of underflow, SOLVE returns a very large value as a root. (The calculator cannot represent infinity, anyway.) D–15 More about Solving File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 337: More About Integration

    E–1 More about Integration File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 338: Conditions That Could Cause Incorrect Results

    Conditions That Could Cause Incorrect Results Although the integration algorithm in the HP 33s is one of the best available, in certain situations it — like all other algorithms for numerical integration — might give you an incorrect answer. The possibility of this occurring is extremely remote.
  • Page 339 , which is virtually the largest number you can key into the calculator. –x Try it and what happens. Enter the function f(x) = xe E–3 More about Integration File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 340 1. The reasons or the incorrect answer becomes apparent from the graph of f(x) over the interval of integration. E–4 More about Integration File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 341 E–5 More about Integration File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 342 (x) Calculated integral of this function will be accurate. f (x) Calculated integral of this function may be accurate. E–6 More about Integration File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 343: Conditions That Prolong Calculation Time

    Selects Equation mode; displays the equation. º "  Integral. (The calculation takes a ∫  minute or two.)    E–7 More about Integration File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 344 Consequently, several more iterations are required over the larger interval to achieve an approximation with the same accuracy, and therefore calculating the integral requires considerably more time. E–8 More about Integration File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 345 These methods enable you to change the function or the limits of integration so that the integrand is better behaved over the interval(s) of integration. E–9 More about Integration File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 347: Messages

    Indicates the "top" of equation memory. The memory    scheme is circular, so    is also the "equation" after the last equation in equation memory. F–1 Messages File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 348 (See appendix B).  The condition checked by a test instruction is not true. (Occurs only when executed from the keyboard.) F–2 Messages File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 349 SOLVE operation was running. ∫ A running program attempted to integrate a program   while a SOLVE operation was running. F–3 Messages File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 350 The self–test or the keyboard test failed, and the calculator requires service. ©  Copyright message displayed after successfully completing the self–test. F–4 Messages File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 351: Operation Index

    1–9 function keyed in an equation; 6–3 starts equation editing; deletes a 12–6 program step. G–1 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 352 º p %CHG Percent change. 4–6 Returns (x – y)(100 ÷ y). π º j Returns the 4–3 approximation 3.14159265359 (12 digits). G–2 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 353 ∑ − ÷ θ , r º ± 4–9 Polar to rectangular coordinates. θ ) to (x, y). Converts (r, G–3 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 354 (antilogarithm). Þ {  } 1–20 Selects display of all significant digits. ¹ i ASIN Arc sine 4–4 –1 Returns sin G–4 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 355 Cube root of argument. 6–15 º · CF n {  } n 13–11 Clears flag n (n = 0 through 11). G–5 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 356 + i z + i z ¹ c à CMPLX – Complex 9–2 subtraction. Returns (z + i z ) – (z G–6 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 357 Combinations of n 4–14 items taken r at a time. Returns n! ÷ (r! (n – r)!). Cosine. 4–3 Returns cos x. G–7 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 358 0 through 11). Causes the exponent display for 1–20 º ] the number being displayed to change in multiples of 3. G–8 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 359 14–1 Selects labeled program as the 14–7 current function (used by SOLVE ∫ FN). º [ Fractional part of x. 4–16 G–9 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 360 Hours, minutes, seconds to hours. Converts x from hours–minutes–seconds format to a decimal fraction. i or 6–4 Value of variable i. G–10 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 361 (increment value) to ccccccc (counter value) and, if the result > fff (final value), skips the next program line. G–11 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 362 (  or  ). 4–4 ¹ . {  } 11–11 Returns the number of sets of data points. G–12 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 363 (decimal point). º © RANDOM Executes the 4–14 RANDOM function. Returns a random number in the range 0 through 1. G–13 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 364 Moves t to the Z–register, z to the Y–register, y to the X–register, and x to the T–register in RPN mode. G–14 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 365 FN=, using initial estimates in variable and x. ® ¥ Inserts a blank space 6–5 character during equation entry. G–15 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 366 º + {  } 11–6 Returns sample standard deviation of y–values: ∑ − ÷ − Tangent. Returns tan x. 4–3 G–16 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 367: Contents

    + 1). X ROOT The argument root of 6–15 argument Returns weighted mean of x 11–4 ) ÷ Σy values: (Σy G–17 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 368 ? º  {≠} 13–7 If x≠0, executes next program line; if x=0, skips the next program line. G–18 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 369 Rectangular to polar 4–10 coordinates. Converts (x, y) to (r, θ ). Power. 4–2 Returns y raised to the x power.  G–19 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 370 Notes: 1. Function can be used in equations. 2. Function appears only in equations. G–20 Operation Index File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 371: Index

    2–13 compared to equations, 12–4 stack operation, 2–4, 9–1 in programs, 12–4 assignment equations, 6–9, 6–10, Algebraic mode, 1–10 6–11, 7–1 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 372 A–4, A–5 converting to, 10–1 turning on and off, 1–1 range of, 10–5 cash flows, 17–1 scrolling, 10–6 catalogs typing, 10–1 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 373 13–6, 13–7, 13–8, in equations, 6–5 13–11, 13–17 in programs, 12–6 constant (filling stack), 2–6 meaning, 1–15 Continuous Memory, 1–1 discontinuities of functions, D–5 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 17.7 x 25.2 cm...
  • Page 374 12–18 EQN annunciator entering, 6–4, 6–8 in equation list, 6–4, 6–6 entering in programs, 12–6 in Program mode, 12–6 evaluating, 6–9, 6–10, 6–12, Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 375 (i), 13–25 unassigned, 13–8 error messages, F–1 flow diagrams, 13–2 errors clearing, 1–4 in programs, 14–5, 14–10 correcting, 2–7, F–1 integrating programs, 14–8 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 17.7 x 25.2 cm...
  • Page 376 1–17, 2–8, 9–2 i, 3–7, 13–21 real–number, 4–1 (i), 3–7, 13–21, 13–22, 13–25 two–number, 1–17, 2–8, 9–3 imaginary part (complex numbers), future balance (finance), 17–1 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 377 4–13 intercept (curve–fit), 11–8, 16–1 math interest (finance), 17–3 complex–number, 9–1 intermediate results, 2–10 general procedure, 1–16 inverse function, 1–17, 9–3 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 17.7 x 25.2 cm...
  • Page 378 4–16 general operation, 1–6 fractions in, 1–21, 5–1 leaving, 1–4, 1–9 in equations, 6–5 list of, 1–7 in programs, 12–6 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 379 4–14 10–5 normal distribution, 16–11 setting response, 13–9, F–3 program catalog, 1–24, 12–20 testing occurrence, 13–9 program labels branching to, 13–2, 13–4, Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 17.7 x 25.2 cm...
  • Page 380 1–24 showing long number, 12–6 deleting all, 1–5 stepping through, 12–9 deleting equations, 12–6, 12–18 stopping, 12–13, 12–14, 12–17 deleting lines, 12–18 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 381 5–8, 12–17 running programs, 12–20 numbers, 4–16 stopping integration, 8–2, 14–8 round–off stopping SOLVE, 7–7, 14–1 fractions, 5–8 and R , 2–2, C–6 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 17.7 x 25.2 cm...
  • Page 382 (calculator), A–5 square–root function, 1–17 shift keys, 1–3 stack. See stack lift sign (of numbers), 1–14, 1–17, 9–3, affected by prompts, 6–13, 10–4 12–12 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 383 4–13 initializing, 11–2 limits for calculator, A–2 one–variable, 11–2 test menus, 13–7 precision, 11–10 testing the calculator, A–4, A–5 sums of variables, 11–11 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 17.7 x 25.2 cm...
  • Page 384 X ROOT arguments, 6–16 number storage, 3–1 X–register of integration, 8–2, 14–7, C–8 affected by prompts, 6–13 polynomials, 12–24 arithmetic with variables, 3–4 program input, 12–12 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...
  • Page 385 2–5 displayed, 2–2 part of stack, 2–1 during programs pause, 12–17 testing, 13–7 exchanging with variables, 3–6 unaffected by VIEW, 12–14 Index– File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 17.7 x 25.2 cm...
  • Page 386 Bij dit produkt zijn batterijen. Wanneer deze leeg zijn, moet u ze niet weggooien maar inleveren aIs KCA. File name 33s-E-Manual-1008-Publication(1st).doc Page : 386 Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm...

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