Instructions for

A Calculus Graph

version 1.01


This program requires 256K of RAM and works on EGA, displaying 2-

dimensional graphs of functions, their first four derivatives and

integrals in vivid color on a color monitor. An 8087 mathematics

coprocessor chip is highly recommended, as this speeds graphing

considerably. The original program, written in Turbo Basic, is

included on this disk for your convenience. The program is quite

self-explanatory, but we shall present a guide to its features.

After the opening credits, you are shown instructions for writing the

functions in AOS or RPN logic. AOS is the logic of Texas Instrument

calculators and is the way one ordinarily writes algebraic

expressions. RPN is the logic of Hewlett-Packard scientific

calculators. Consult these manufacturers if you need instructions in

the logics. AOS is easier for the programmer to write, but the

graphs will run faster if the functions are written in RPN,

especially with longer functions. In RPN logic, "5 2 sin +" produces

5 + sin 2 = 5.909..., for example. This program does not recognize

the "enter" instruction: "x" recalls the value of x whenever it

appears, and "sto1", "sto2", and "sto3" allow you to store three

values for recall later in the expression (so "x sqr y sqr+sto1 chs

exp rcl1/" computes

2 2
-(x + y ) 2 2
e /(x + y ),

for example).

In either logic the delimiters are spaces, the operations +, -,

*, /, ^, and parentheses (, and ) (so the displayed expression above

would be entered as "exp(-x sqr-y sqr)/(x sqr+y sqr)", with

additional spaces inserted as desired for clarity). Do not put

spaces in the middle of a word ("ex p" will not be read as "exp").

Available functions include the arithmetic operations of

addition +, subtraction -, multiplication *, division /, and raising

to a power ^. Thus 2 ^ 3 in AOS logic (or 2 3 ^ in RPN) produces 2

to the third power or 8. Other functions include absolute value

(abs), sign (sgn) (sgn x = 1 if x > 0, sgn x = 0 if x = 0, and sgn x

= -1 if x < 0), greatest integer (int) (int x returns the largest

integer less than or equal to x), square root (sqrt), cube root

(cuberoot), square (sqr), and cube (cube). Trigonometric functions

include sin, cos, tan, arctan, all given in radian measure. Other

transcendental functions available are natural logarithm (ln), base

ten logarithm (log), and the natural exponential (exp).

Next you will be shown a graphing menu. Near the top right of

the screen is a logic statement. When this is highlighted,

toggles between AOS and RPN logic. "Insert Mode" toggles between

insert and overwrite (for editing functions) by -v or .

At the bottom of the screen, "Quit" toggles between yes and no. If

yes, then terminates the program and returns you to DOS.

"Return to opening menu" also toggles between yes and no. if yes,

then returns to the opening statement so you can read the

function instructions again. All variable choices are

cancelled. Above that are two statements. On the right side of

the menu is a set of general instructions for using the menu.

Initial values have been selected when a menu appears. These

may be left alone, if they are o.k. Otherwise highlight the item by

using the up and down arrow keys to move from one item to the next.

Then hit to toggle items that can be toggled, or enter new

functions or values by typing (lower case letters only, please) the

new value or function. Existing functions can be edited. Highlight

the function. Then hit either left or right arrow. A green block

appears at the highlighted character. Typing characters now either

inserts or overwrites, according to the insert toggle setting. Use

the left and right arrows to move to the desired location. Use

or -g to delete the character at the cursor, backspace to

delete the preceding character. When done, the up and down arrows

end the editing session and move you to the next block. When all

values have been chosen as desired, hit . "Quit" takes first

precedence, "Return to opening menu" is second. Otherwise the graph

you have selected will be plotted. After a graph plots, the function

equation will be displayed at the bottom of the graph. Then hit any

key to continue with either the integral or the derivative program.

In the integral program, the graph of the indefinite integral

will be drawn in blue, along with the area in brown that represents

the definite integral you have chosen. The constant of integration

is taken so that the integral curve crosses the x-axis at the lower

limit of the definite integral. Then hit any key to return to the

menu.

In the derivative program, after the original function is

graphed, if you hit q at any time, you will be returned to the menu.

If you hit t after the function draws, you can watch a short colored

tangent line move along the curve while the graph of the derivative

is drawn in green. If you hit any other key instead of t or q, the

derivative will be drawn quickly without the moving tangent line.

After the derivative is drawn, hit any key to draw a second

derivative and then a third and then a fourth derivative. If you do

not wish to see the higher order derivatives, hit q. Then hit any

key to return to the menu.

To quit the program, hit the up arrow to highlight "Quit", hit

, and .


"Reasonable" values have been selected when the menu displays.

The screen has 640 pixels in EGA horizontally. Plotting every 3rd to

10th pixel is generally sufficient. This value can be any positive

integer, but in integrals this value is automatically reset to 1 for

correct calculation of definite integrals. In all graphs, straight

lines are drawn between plotted points, so the smaller this number

is, the better the graph looks. You should always use coordinates

that increase from minimum to maximum from left to right and down to

up. Limits of integration, however, can be in decreasing.

This program is supplied as shareware. You are encouraged to

pass it along to others, along with the original Turbo Basic listing

and this file. If you use this program, you are asked to mail $5 to

the author, listed below. If you wish the latest version of this

program on disk, please send $10. The first registered owner sending

any valid correction to the program will receive a free update disk.

This program is distributed "as is." No warrantees are made.

Send your $5 or $10 to

Clayton W. Dodge
Mathematics Department
University of Maine
Orono, Maine 04469
ACG, ver. 1.01
June 7, 1988