Complex Number Calculations; Equation Solvers; Matrix Calculations; Vector Calculations - Sharp EL-W516T Operation Manual

–
y
Mean of samples (
sy
Sample standard deviation (
s Sample variance (
y
2
sy
Population standard deviation (
s
y Population variance (
2
Σy
Sum of samples (
Σy
Sum of squares of samples (
2
2
Σx y
Sum of products of samples (
Σx
y
Sum of products of samples (
2
Σx
Sum of 3rd powers of samples (
3
Σx
Sum of 4th powers of samples (
4
ymin Minimum value of samples (
ymax Maximum value of samples (
Q
First quartile of sample (
1
Med
Median of sample (
3
Q
Third quartile of sample (
3
r
Correlation coefficient (Except Quadratic regression)
a
Coefficient of regression equation
b
Coefficient of regression equation
4
c
Coefficient of quadratic regression equation
R
2
Coefficient of determination (Quadratic regression)
r
2
Coefficient of determination (Except Quadratic regression)
STAT Menu
After closing the input table, you can view statistical values, view
regression coefficient values, and specify statistical variables from the
STAT menu (; 8).
; 8 0: Display statistical values
; 8 1: Display regression coefficient values
; 8 2: Specify statistical value variables
; 8 3: Specify statistical value (
; 8 4: Specify max/min value variables
; 8 5: Specify regression coefficient variables
Notes:
• List display of regression coefficient values and specification of
regression coefficient variables do not appear in single-variable
statistical calculation.
x y
• Estimated values ' and ' are specified with the keys (@ V, @
x
U). If there are two ' values, you can specify
menu ( ; 8 5) to obtain the values separately.
• In the statistical value and regression coefficient value lists, you cannot
return to the menu by pressing N.

Statistical Calculation Formulas

An error will occur when:
• The absolute value of the intermediate result or calculation result is
×
equal to or greater than 1 10 100 .
• The denominator is zero.
• An attempt is made to take the square root of a negative number.
• No solution exists in the quadratic regression calculation.

Normal Probability Calculations

In STAT mode, the three probability density functions can be accessed
under the MATH menu, with a random number used as a normal
distribution variable.
Notes:
• P(t), Q(t), and R(t) will always take positive values, even when t < 0,
because these functions follow the same principle used when solving
for an area.
• Values for P(t), Q(t), and R(t) are given to six decimal places.
• The standardization conversion formula is as follows:
-
x x
t = —
s
x
TABLE MODE
You can see the changes in values of one or two functions using TABLE
x
mode.
Setting a table
1. Press b 2 to enter TABLE mode.
2. Enter a function (Function1), and press e.
3. If needed, enter the 2nd function (Function2) and press e.
4. Enter a starting value (X_Start:), and press e.
The default starting value is 0.
5. Enter a step value (X_Step:). The default step value is 1.
• You can use u and d to move the cursor between the starting
value and step value.
6. Press e when you finish entering a step value. A table with a
variable X and the corresponding values (ANS column) appears,
displaying 3 lines below the starting value.
If you entered two functions, the ANS1 and ANS2 columns appear.
You can use u and d to change the X value and see its
corresponding values in table format.
• The table is for display only and you cannot edit the table.
• The values are displayed up to 7 digits, including signs and a decimal
point.
• Press l or r to move the cursor to ANS column (ANS1 and ANS2
columns if you entered two functions) or X column.
• Full digits of the value on the cursor are displayed on the bottom right.
Notes:
• In a function, only "X" can be used as a variable, and other variables
are all regarded as numbers (stored into the variables).
• Irrational numbers such as and
r
value or a step value. You cannot enter 0 or a negative number as a
step value.
• You can use WriteView editor when inputting a function.
• The following features are not used in TABLE mode: coordinate
conversions, conversion between decimal and sexagesimal numbers,
and angular unit conversions.
• It may take time to make a table, or "-------" may be displayed, depending on
the function entered or conditions specified for the variable X.
• Please note that when making a table, the values for variable X are
rewritten.
• Press @ Z or mode selection to return to the initial screen of the
mode, and return to the default values for the starting value and step value.
y

COMPLEX NUMBER CALCULATIONS

data)
y
data)
To carry out addition, subtraction, multiplication, and division using
y
data)
complex numbers, press b 3 to select COMPLEX mode.
Results of complex number calculations are expressed using two
y
data)
systems:
y
data)
@ E: Rectangular coordinate system
1
y
data)
@ u: Polar coordinate system
2
y
data)
x, y
)

Complex Number Entry

x , y
2
)
Rectangular coordinates
1
x
data)
x
data)
Polar coordinates
2
y
data)
y
data)
• On selecting another mode, the imaginary part of any complex number
x
data)
stored in the independent memory (M) and the last answer memory
x
data)
(ANS) will be cleared.
x
• A complex number expressed in rectangular coordinates with the
data)
y-value equal to zero, or expressed in polar coordinates with the angle
equal to zero, is treated as a real number.
• From the MATH menu, you can obtain the complex conjugate (conj( ), the
argument of a complex number (arg( ), the real part of a complex number (real(
), and the imaginary part of a complex number (img( ).

EQUATION SOLVERS

The results obtained by these functions may include a margin of error.

Simultaneous Linear Equations

Simultaneous linear equations with two unknowns (2-VLE) or with three
unknowns (3-VLE) may be solved using the following functions.
2-VLE: b 4 0
1
3-VLE: b 4 1
Σ
2
related) variables
• If the determinant D = 0, an error occurs.
• If the absolute value of an intermediate result or calculation result is 1
×
x x
1' and 2' from the STAT Solving simultaneous linear equations
1. Press b 4 0 or b 4 1.
2. Enter the value for each coefficient (
29
3. When all coefficients have been entered, press e to solve the
30

Quadratic and Cubic Equations

Quadratic (
equations may be solved using the following functions.
Quadratic equation solver: b 4 2
1
Cubic equation solver: b 4 3
2
• If there are two or more solutions, those solutions are also shown.
• If calculable, you can also obtain the minimum value (when a > 0) and
the maximum value (when a < 0) of a quadratic function (
+
Solving quadratic and cubic equations
• Press b 4 2 or b 4 3.
• Coefficients for these equations can be entered in the same manner as
31 those for simultaneous linear equations.
• When using the QUADRATIC equation solver, continue by pressing
e (or d) to display the minimum value or maximum value. To
return to the solution, press u with the minimum value or maximum
value displayed.
• To return to the coefficient entry screen when the solution (or
minimum/maximum value) is displayed, press e or j.
• To clear all the coefficients, press @ Z .

MATRIX CALCULATIONS

You can store and calculate up to four matrices.
Entering and Storing Matrices
1. Press b 5 to enter MATRIX mode.
2. Press N 1 to bring up the matrix entry screen.
3. Define the matrix dimensions (up to four rows by four columns) by
p
can also be entered into a starting
4. Enter each element in the matrix by entering a value in the entry field
5. When you have entered a value for each element, press j to exit
6. Press N 3 and select a memory (matA–matD) to store the
(The symbol appears.)
(The symbol appears.)
x-coordinate + y-coordinate O
or x-coordinate + O y-coordinate
q
r @ Q
q
r : absolute value : argument
a x + b y = c
1 1 1
D =
a x + b y = c
2 2 2
a x + b y + c z = d
1 1 1 1
a x + b y + c z = d D =
2 2 2 2
a x + b y + c z = d
3 3 3 3
10 100 or more, an error occurs.
a
, etc.).
1
• Coefficients can be entered using ordinary arithmetic operations.
• To clear the entered coefficient, press j.
• Press u or d to move the cursor up or down through the
coefficients. Press @ u or @ d to jump to the first or
last coefficient.
equation.
• While the solution is displayed, press e or j to return to the
coefficient entry display. To clear all the coefficients, press @ Z .
+ b x + c = ax + b
ax
2 0 ) or cubic ( 3
c
) .
• Any matrix data remaining in the buffer, along with any previously
entered, loaded, or calculated matrix data, will be displayed.
entering the required dimensions using the number keys and pressing
e.
Matrix dimensions (row
Element fields
Entry field
Matrix entry screen (example)
and pressing e.
• Each matrix element can display up to seven digits (the decimal
point counts as one digit). If an element exceeds seven digits in
length, it may be displayed in exponent notation within the matrix.
• A maximum of three rows by three columns can be displayed at
one time. Use u, d, l, and r to move the cursor
through the matrix.
the matrix entry screen.
newly-created matrix in.
4/9
Modifying a stored matrix
32
1. To load a stored matrix into the matrix entry screen, press N
2, then select the memory (matA–matD) that you wish to
modify.
• Loading new data into the screen will automatically replace any
data that may already exist there.
2. Modify the values of elements in the matrix, and press e after
each one.
• If you wish to modify the number of rows or columns, first press
j N 1. You can then enter new values for the matrix
dimensions.
3. When you have finished making changes, press j to exit the
matrix entry screen.
4. Press N 3 and select a memory (matA–matD) to store the
newly-created matrix in.
Using Matrices in Calculations
Matrices stored in memories (matA–matD) can be used in arithmetic
calculations (with the exception of division between matrices) and
calculations that use
matrix-specific functions that are available in the MATH menu.
det matrix name
trans matrix name
identity value
33
dim (matrix name, row, column) Returns a matrix with dimensions
fill (value, row, column)
rand_mat (row, column)
a b
1 1
a b
ref(matrix name)
2 2
rref(matrix name)
a b c
1 1 1
Notes:
a b c
2 2 2
• When the matrix entry screen is displayed, you cannot perform
a b c
3 3 3
matrix calculations because the MATH menu is not available.
• If the calculation result is a matrix, it will be displayed in the matrix
entry screen (note that this replaces any existing data in the buffer).
To store the calculation result, first press j to exit the matrix
entry screen. Press N 3 and select a memory (matA–matD)
to store the newly-created matrix in.
• When the calculation results are in matrix form, pressing neither
l nor r will bring you back to the original expression.

VECTOR CALCULATIONS

You can store and calculate up to four vectors of two or three
dimension in VECTOR mode.
Entering and Storing Vectors
Before performing vector calculations, a vector must be created.
Follow the steps below to enter and store vectors.
1. Press b 6 to enter VECTOR mode.
2. Press N 1 to bring up the vector entry screen.
x + cx + d = • Any vector data remaining in the buffer, along with any previously
2 0 )
entered, loaded, or calculated vector data, will be displayed.
3. Define the vector dimensions (2 dimensions or 3 dimensions) by
using the number keys and pressing e.
4. Enter each element in the vector by entering a value in the entry
field and pressing e.
+ b x • Each vector element can display up to seven digits (the decimal
y ax
=
2
point counts as one digit).
If an element exceeds seven digits in length, it may be displayed
in exponent notation within the vector.
5. When you have finished entering a value for each element, press
j to exit the vector entry screen.
6. Press N 3 and select a memory (vectA–vectD) to store the
newly-created vector in.
Modifying a stored vector
1. To load a stored vector into the vector entry screen, press N
2, then select the memory (vectA–vectD) that you wish to
modify.
• Loading new data into the screen will automatically replace any
data that may already exist in the vector entry screen.
2. Modify the values of elements in the vector, and press e after
34
each one.
• If you wish to modify the number of dimensions, first press
j N 1. You can then enter new values for the vector
dimensions.
3. When you have finished making changes, press j to exit the
vector entry screen.
4. Press N 3 and select a memory (vectA–vectD) to store the
newly-created vector in.
Using Vectors in Calculations
vectors stored in memories (vectA–vectD) can be used in arithmetic
calculations (with the exception of division between vectors). You can
also use the following vector-specific functions that are available in the
×
column)
MATH menu.
DotPro(vector name, vector name)
CrossPro(vector name, vector name)
Angl(vector name, vector name)
Unit(vector name)
Notes:
• You can use "abs" function (abs vector name) for the absolute value.
• When multiplying vectors, the cross product is calculated.
• When the vector entry screen is displayed, press j and then you
perform vector calculations.
• If the calculation result is a vector, it will be displayed in the vector
entry screen.
To store the calculation result, first press j to exit the vector
entry screen. Press N 3 and select a memory (vectA–vectD)
to store the newly-created vector in.
• When the calculation results are in vector form, pressing neither
l nor r will bring you back to the original expression.
x x x -
3 , 2 , and 1 . You can also use the following
Returns the determinant of a
square matrix.
Returns the matrix with the
columns transposed to rows and
the rows transposed to columns.
Returns the identity matrix with
specified value of rows and columns.
changed as specified.
Fills each element with a specified
value.
Returns a random matrix with
specified values of rows and columns.
Transform to row echelon form.
Transform to reduced row echelon
form.
Returns the dot product.
Returns the cross product.
Returns the angle.
Returns the unit vector.
35