Sharp EL5020 Operation Manual - Page 3

Metric Conversions

See the quick reference card and the English manual reverse side.

Unit conversions can be performed in the normal mode (when not

set to binary, pental, octal, or hexadecimal), equation mode and

statistics modes.

Calculations Using Engineering Prefixes

Calculation can be executed in the normal mode (excluding N-

base) using the following 9 types of prefixes.

Modify Function

Calculation results are internally obtained in scientific notation

with up to 14 digits for the mantissa. However, since calculation

results are displayed in the form designated by the display nota-

tion and the number of decimal places indicated, the internal

calculation result may differ from that shown in the display. By

using the modify function, the internal value is converted to match

that of the display, so that the displayed value can be used

without change in subsequent operations.

Solver Function

The

x

value can be found that reduces an entered equation to “0”.

•

This function uses Newton’s method to obtain an approxima-

tion. Depending on the function (e.g. periodic) or ‘Start’ value,

an error may occur (Error 2) due to there being no convergence

to the solution for the equation.

•

The value obtained by this function may include a margin of

error. If it is larger than acceptable, recalculate the solution

after changing ‘Start’ and

dx

values.

•

Change the ‘Start’ value (e.g. to a negative value) or

dx

value

(e.g. to a smaller value) if:

•

no solution can be found (Error 2).

•

more than two solutions appear to be possible (e.g. a cubic

equation).

•

to improve the arithmetic precision.

•

The calculation result is automatically stored in the X memory.

[Performing Solver function]

Q

Press

m0

.

W

Input a formula with an

x

variable.

E

Press

∑0

.

R

Input ‘Start’ value and press

®

. The default value is “0”.

T

Input

dx

value (minute interval).

Y

Press

®

.

SIMULATION CALCULATION (ALGB)

If you have to find a value consecutively using the same formula,

such as plotting a curve line for 2

x

2

+ 1, or finding the variable for

2

x

+ 2

y

=14, once you enter the equation, all you have to do is to

specify the value for the variable in the formula.

Usable variables: A-F, M, X and Y

Unusable functions:

Random function

•

Simulation calculations can only be executed in the normal

mode.

•

Calculation ending instructions other than

=

cannot be used.

Performing Calculations

Q

Press

m0

.

W

Input a formula with at least one variable.

E

Press

@≤

.

R

Variable input screen will appear. Input the value of the flashing

variable, then press

®

to confirm. The calculation result will

be displayed after entering the value for all used variables.

•

Only numerical values are allowed as variables. Input of

formulas is not permitted.

•

Upon completing the calculation, press

@≤

to per-

form calculations using the same formula.

•

Variables and numerical values stored in the memories will be

displayed in the variable input screen. To change a numerical

value, input the new value and press

®

.

•

Performing simulation calculation will cause memory locations

to be overwritten with new values.

STATISTICAL CALCULATIONS

Press

m1

to select the statistics mode. The seven statisti-

cal calculations listed below can be performed. After selecting the

statistics mode, select the desired sub-mode by pressing the number

key corresponding to your choice.

To change statistical sub-mode, reselect statistics mode (press

m1

), then select the required sub-mode.

0

(SD)

:

Single-variable statistics

1

(LINE)

:

Linear regression calculation

2

(QUAD)

:

Quadratic regression calculation

3

(EXP)

:

Exponential regression calculation

4

(LOG)

:

Logarithmic regression calculation

5

(PWR)

:

Power regression calculation

6

(INV)

:

Inverse regression calculation

The following statistics can be obtained for each statistical calcula-

tion (refer to the table below):

Single-variable statistical calculation

Statistics of

Q

and value of the normal probability function

Linear regression calculation

Statistics of

Q

and

W

and, in addition, estimate of

y

for a given

x

(estimate

y

´

) and estimate of

x

for a given

y

(estimate

x

´

)

Exponential regression, Logarithmic regression,

Power regression, and Inverse regression calculation

Statistics of

Q

and

W

. In addition, estimate of

y

for a given

x

and

estimate of

x

for a given

y

. (Since the calculator converts each

formula into a linear regression formula before actual calculation

takes place, it obtains all statistics, except coefficients

a

and

b

,

from converted data rather than entered data.)

Quadratic regression calculation

Statistics of

Q

and

W

and coefficients

a

,

b

,

c

in the quadratic

regression formula (

y

=

a

+

bx

+

cx

2

). (For quadratic regression

calculations, no correlation coefficient (

r

) can be obtained.) When

there are two

x

´

values, press

@≠

.

When performing calculations using

a

,

b

and

c

, only one numeric

value can be held.

¯

x

Mean of samples (

x

data)

sx

Sample standard deviation (

x

data)

Q

σ

x

Population standard deviation (

x

data)

n

Number of samples

Σ

x

Sum of samples (

x

data)

Σ

x

2

Sum of squares of samples (

x

data)

¯

y

Means of samples (

y

data)

sy

Sample standard deviation (

y

data)

σ

y

Population standard deviation (

y

data)

Σ

y

Sum of samples (

y

data)

W

Σ

y

2

Sum of squares of samples (

y

data)

Σ

xy

Sum of products of samples (

x

,

y

)

r

Correlation coefficient

a

Coefficient of regression equation

b

Coefficient of regression equation

c

Coefficient of quadratic regression equation

•

Use

K

and

R

to perform a STAT variable calculation.

Data Entry and Correction

Entered data are kept in memory until

@c

or mode selec-

tion. Before entering new data, clear the memory contents.

[Data Entry]

Single-variable data

Data

k

Data

&

frequency

k

(To enter multiples of the same data)

Two-variable data

Data

x

&

Data

y

k

Data

x

&

Data

y

&

frequency

k

(To enter multiples

of the same data

x

and

y

.)

•

Up to 100 data items can be entered. With the single-variable

data, a data item without frequency assignment is counted as

one data item, while an item assigned with frequency is stored as

a set of two data items. With the two-variable data, a set of data

items without frequency assignment is counted as two data items,

while a set of items assigned with frequency is stored as a set of

three data items.

[Data Correction]

Correction prior to pressing

k

immediately after a data entry:

Delete incorrect data with

ª

, then enter the correct data.

Correction after pressing

k

:

Use

[]

to display the data previously entered.

Press

]

to display data items in ascending (oldest first)

order. To reverse the display order to descending (latest first),

press the

[

key.

Each item is displayed with

‘

Xn=

’

,

‘

Yn=

’

, or

‘

Nn=

’

(

n

is the sequen-

tial number of the data set).

Display the data item to modify, input the correct value, then

press

k

. Using

&

, you can correct the values of the data

set all at once.

•

To delete a data set, display an item of the data set to delete,

then press

@J

. The data set will be deleted.

•

To add a new data set, press

ª

and input the values, then

press

k

.

Statistical Calculation Formulas

In the 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

•

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.

SIMULTANEOUS LINEAR EQUATIONS

Simultaneous linear equation with two unknowns (2-VLE) or with

three unknowns (3-VLE) may be solved using this function.

Q

2-VLE:

m20

W

3-VLE:

m21

•

If the determinant D = 0, an error occurs.

•

If the absolute value of an intermediate result or calculation result

is 1

×

10

100

or more, an error occurs.

•

Coefficients ( a

1

, etc.) can be entered using ordinary arithmetic

operations.

•

To clear the entered coefficients, press

@c

.

•

Pressing

®

when the determinant D is in the display recalls

the coefficients. Each time

®

is pressed, a coefficient is

displayed in the order of input, allowing the entered coefficients

to be verified (by pressing

@®

, coefficients are displayed

in reverse order.) To correct a particular coefficient being dis-

played, enter the correct value and then press

®

.

QUADRATIC AND CUBIC EQUATION SOLVERS

Quadratic (

ax

2

+ bx + c = 0

) or cubic (

ax

3

+ bx

2

+ cx + d = 0

) equation

may be solved using this function.

Q

Quadratic equation solver:

m22

W

Cubic equation solver:

m23

•

Press

®

after entering each coefficient.

•

The result will be displayed by pressing

®

after entering all

coefficients. When there are more than 2 results, the next solu-

tion will be displayed.

•

When the result is an imaginary number,

“

xy

”

symbol will appear.

The display can be switched

between imaginary and real parts

by pressing

@≠

.

COMPLEX NUMBER CALCULATIONS

To carry out addition, subtraction, multiplication, and division using

complex numbers, press

m3

to select the complex number

mode.

Results of complex number calculations are expressed in two modes:

Q

@}

: Rectangular coordinate mode (

xy

appears.)

W

@{

: Polar coordinate mode (

r

θ

appears.)

Complex number entry

Q

Rectangular coordinates

x-coordinate

+

y-coordinate

Ü

or

x-coordinate

+Ü

y-coordinate

W

Polar coordinates

r

Ö

θ

r: absolute value

θ

: argument

•

On selecting another mode, the imaginary part of any complex

number stored in the independent memory (M) will be cleared.

•

A complex number expressed in rectangular coordinates with the

y-value equal to zero, or expressed in polar coordinates with the

angle equal to zero, is treated as a real number.

•

Press

∑0

to return the complex conjugate of the speci-

fied complex number.

ERROR AND CALCULATION RANGES

Errors

An error will occur if an operation exceeds the calculation ranges,

or if a mathematically illegal operation is attempted. When an error

occurs, pressing

<

(or

>

) automatically moves the cursor

back to the place in the equation where the error occurred. Edit the

equation or press

ª

to clear the equation.

Type

Regression formula

Linear

y

=

a

+

bx

Exponential

y

=

a

•

e

bx

Logarithmic

y

=

a

+

b

•

ln

x

Power

y

=

a

•

x

b

Inverse

y

=

a

+

b

—

Quadratic

y

=

a

+

bx

+

cx

2

1

x

No.

Remarks

1

in

: inch

2

cm

: centimeter

3

ft

: foot

4

m

: meter

5

yd

: yard

6

m

: meter

7

mile

: mile

8

km

: kilometer

9

n mile

: nautical mile

10

m

: meter

11

acre

: acre

12

m

2

: square meter

13

oz

: ounce

14

g

: gram

15

lb

: pound

16

kg

: kilogram

17

°

F

: Degree Fahrenheit

18

°

C

: Degree Celsius

19

gal (US) : gallon (US)

20

l

: liter

21

gal (UK) : gallon (UK)

22

l

: liter

No.

Remarks

23

fl oz(US): fluid ounce(US)

24

m

l

: milliliter

25

fl oz(UK): fluid ounce(UK)

26

m

l

: milliliter

27

J

: Joule

28

cal

: calorie

29

J

: Joule

30

cal

15

: Calorie (15n

°

C)

31

J

: Joule

32

cal

IT

: I.T. calorie

33

hp

: horsepower

34

W

: watt

35

ps

: French horsepower

36

W

: watt

37

38

Pa

: Pascal

39

atm

: atmosphere

40

Pa

: Pascal

41

(1 mmHg = 1 Torr)

42

Pa

: Pascal

43

44

J

: Joule

Prefix

Operation

Unit

k

(kilo)

∑10

10

3

M

(Mega)

∑11

10

6

G

(Giga)

∑12

10

9

T

(Tera)

∑13

10

12

m

(milli)

∑14

10

–

3

μ

(micro)

∑15

10

–

6

n

(nano)

∑16

10

–

9

p

(pico)

∑17

10

–

12

f

(femto)

∑18

10

–

15

Sharp EL5020 Operation Manual - Page 3

Quadratic And Cubic Equation Solvers

Page 3 highlights