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Computer Algebra
System and Tutorial
Modes
7-1
Using the CAS (Computer Algebra System) Mode
7-2
Algebra Mode
7-3
Tutorial Mode
7-4
Algebra System Precautions
Chapter
19990401
7

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  • Page 1

    Chapter Computer Algebra System and Tutorial Modes Using the CAS (Computer Algebra System) Mode Algebra Mode Tutorial Mode Algebra System Precautions 19990401...

  • Page 2

    7-1-1 Using the CAS (Computer Algebra System) Mode 7-1 Using the CAS (Computer Algebra System) Mode On the Main Menu, select the CAS icon to enter the CAS Mode. The following table shows the keys that can be used in the CAS Mode. COPY PASTE H-COPY...

  • Page 3

    7-1-2 Using the CAS (Computer Algebra System) Mode If all the result does not fit on the display, use the cursor keys to scroll it. k k k k k Performing an Algebra Mode Operation There are two methods that you can use for input in the Algebra Mode. •...

  • Page 4: Formula Memory

    7-1-3 Using the CAS (Computer Algebra System) Mode k k k k k Manual Formula and Parameter Input You can use the function menus, K key, and J key in combination to input formulas and parameters as described below. • 3(EQUA)b(INEQUA) •...

  • Page 5

    7-1-4 Using the CAS (Computer Algebra System) Mode k Function Memory and Graph Memory Function memory lets you store functions for later recall when you need them. With graph memory, you can store graphs in memory. Press the J key and then input the name of the graph.

  • Page 6

    7-1-5 Using the CAS (Computer Algebra System) Mode k Answer (Ans) Memory and Continuous Calculation Answer (Ans) memory and continuous calculation can be used just as with standard calculations. In the Algebra Mode, you can even store formulas in Ans memory. ○...

  • Page 7

    7-1-6 Using the CAS (Computer Algebra System) Mode SET UP Items u u u u u Angle ... Unit of angular measurement specification • {Deg}/{Rad} ... {degrees}/{radians} u u u u u Answer Type ... Result range specification • {Real}/{Cplx} ... {real number}/{complex number} u u u u u Display ...

  • Page 8

    7-1-7 Using the CAS (Computer Algebra System) Mode Algebra Command Reference The following are the abbreviations used in this section. • Exp ... Expression (value, formula, variable, etc.) • Eq ... Equation • Ineq ... Inequality Anything enclosed within square brackets can be omitted. u expand Function: Expands an expression.

  • Page 9

    7-1-8 Using the CAS (Computer Algebra System) Mode u solve Function: Solves an equation. Syntax: solve( Exp [,variable] [ ) ] solve( {Exp-1,..., Exp-n}, {variable-1,...,variable-n} [ ) ] ○ ○ ○ ○ ○ Example To solve AX + B = 0 for X 1(TRNS)e(solve)av(A)v+ –...

  • Page 10

    7-1-9 Using the CAS (Computer Algebra System) Mode u trigToExp (trigToE) Function: Transforms a trigonometric or hyperbolic function to an exponential function. Syntax: trigToExp( Exp [ ) ] ○ ○ ○ ○ ○ Example To convert cos(iX) to an exponential function —...

  • Page 11

    7-1-10 Using the CAS (Computer Algebra System) Mode u combine (combin) Function: Reduces a fraction. Syntax: combine( {Exp/Eq/Ineq} [ ) ] ○ ○ ○ ○ ○ Example To reduce the fraction (X + 1) / (X + 2) + X (X + 3) X 3 + 5X 2 + 7X + 1 1(TRNS)h(combin)(v+b)/ X + 2...

  • Page 12

    7-1-11 Using the CAS (Computer Algebra System) Mode u approx Function: Produces a numerical approximation for an expression. Syntax: approx Exp ○ ○ ○ ○ ○ Example To obtain a numerical value for 2 1(TRNS)l(approx)!x( 1.414213562 k About approx Using approx affects the number of digits used to display a calculation result and the way calculations that include variables are performed in the CAS Mode.

  • Page 13

    7-1-12 Using the CAS (Computer Algebra System) Mode u diff Function: Differentiates an expression. Syntax: diff( Exp [, variable, order, derivative] [ ) ] diff( Exp, variable [, order, derivative] [ ) ] diff( Exp, variable, order [, derivative] [ ) ] ○...

  • Page 14

    7-1-13 Using the CAS (Computer Algebra System) Mode u Σ Function: Calculates a sum. Syntax: Σ( Exp, variable, start value, end value [ ) ] ○ ○ ○ ○ ○ To calculate the sum as the value of X in X 2 changes from X = 1 Example through X = 10 2(CALC)e(Σ)vx,v,b,baw...

  • Page 15

    7-1-14 Using the CAS (Computer Algebra System) Mode u tanLine (tanLin) Function: Returns the expression for a tangent line. Syntax: tanLine( Exp, variable, variable value at point of tangency [ ) ] ○ ○ ○ ○ ○ To determine the expression for a line tangent with X 3 when X = 2 Example 2(CALC)i(tanLin)vMd,v,cw 12X –...

  • Page 16

    7-1-15 Using the CAS (Computer Algebra System) Mode u rclEqn Function: Recalls multiple eqn memory contents. Syntax: rclEqn( memory number [ , ..., memory number] [ ) ] ○ ○ ○ ○ ○ Example To recall the contents of equation memory 2 and equation memory 3 3(EQUA)c(rclEqn)c,dw 3X –...

  • Page 17

    7-1-16 Using the CAS (Computer Algebra System) Mode u eliminate (elim) Function: Assigns an expression to a variable. Syntax: eliminate( {Eq/Ineq} -1, variable, Eq-2 [ ) ] ○ ○ ○ ○ ○ Example To transform Y = 2X + 3 to X= and then substitute 2X + 3Y = 5 3(EQUA)g(elim)ca+(X)+da-(Y)!.(=) f,a+(X),a-(Y)!.(=) ca+(X)+dw...

  • Page 18

    7-1-17 Using the CAS (Computer Algebra System) Mode u clear (clrVar) Function: Clears the contents of specific equation (A to Z, , θ ).* Syntax: clear( variable [ ) ] clear( {variable list} [ ) ] ○ ○ ○ ○ ○ Example To clear the contents of variable A 6(g)1(CLR)b(clrVar)av(A)w...

  • Page 19

    7-2-1 Algebra Mode 7-2 Algebra Mode The CAS Mode automatically provides you with the final result only. The Algebra Mode, on the other hand, lets you obtain intermediate results at a number of steps along the way. On the Main Menu, select the ALGEBRA icon to enter the Algebra Mode. The screens in this mode are the same as those in the CAS Mode.

  • Page 20

    7-2-2 Algebra Mode u absExpand (absExp) Function: Divides an expression that contains an absolute value into two expressions. Syntax: absExpand( {Eq/Ineq} [ ) ] ○ ○ ○ ○ ○ Example To strip the absolute value from | 2X – 3 | = 9 3(EQUA)i(absExp)K1(Abs)( 2X –...

  • Page 21

    7-3-1 Tutorial Mode 7-3 Tutorial Mode On the Main Menu, select the TUTOR icon to enter the Tutorial Mode. k Tutorial Mode Flow 1. Specify the expression type. 2. Define the expression. 3. Specify the solve mode. k Specifying the Expression Type Entering the Tutorial Mode displays a menu of the following expression types.

  • Page 22

    7-3-2 Tutorial Mode The following shows the formulas available for each type of expression. Linear Equation — 6 Types • AX = B • X + A = B • AX + B = C • AX + B = CX + D •...

  • Page 23

    7-3-3 Tutorial Mode k Defining the Expression In this step, you specify coefficients and define the expression. You can select any of the three following methods for specifying coefficients. • {RAND} ... {random generation of coefficients} • {INPUT} ... {key input of coefficients} •...

  • Page 24: Verify Mode

    7-3-4 Tutorial Mode k Specifying the Solve Mode You can select one of the following three solve modes for the displayed expression. • {VRFY} ... {Verify Mode} In this mode, you input a solution for verification of whether or not it is correct. It provides a good way to check solutions you arrive at manually.

  • Page 25

    7-3-5 Tutorial Mode You can press 4(MANU) to change to the Manual Mode or 5(AUTO) to change to the Auto Mode. ○ ○ ○ ○ ○ Example To solve 4X = 8 in the Verify Mode (Linear Equation)(AX = B) 2(INPUT)ewiw6(EXE) 4(VRFY)cw 6(JUDG)

  • Page 26

    7-3-6 Tutorial Mode k Manual Mode Press 5(MANU) to enter the Manual Mode. As with the Algebra Mode, the screen is divided between an input area and a display area. This means you can select Algebra Mode commands from the function menu, transform the expression, and solve it.

  • Page 27

    7-3-7 Tutorial Mode ○ ○ ○ ○ ○ Example = 16 True (X = 2, X = – 2) Besides “TRUE” the messages shown below can also appear as the result of verification. “CAN NOT JUDGE” appears in the Manual Mode, while the other messages appear in both the Verify Mode and Manual Mode.

  • Page 28

    7-3-8 Tutorial Mode k Auto Mode Press 6(AUTO) to enter the Auto Mode. In the Simultaneous Equation Mode, you must also select SBSTIT (Substitution Method) or ADD-SU (Addition/Subtraction Method). The Substitution Method first transforms the equation to the format Y = aX + b, and substitutes the other expression to Y.* The Addition/Subtraction Method multiplies both sides of the expression by the same value to isolate the coefficient X (or Y).

  • Page 29

    7-4-1 Algebra System Precautions 7-4 Algebra System Precautions • If an algebraic operation cannot be performed for some reason, the original expression remains on the display. • It may take considerable time to perform an algebraic operation. Failure of a result to appear immediately does not indicate malfunction of the computer.

  • Page 30

    19990401...

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