MATH 163, Spring 2001 Due Date: Name(s):
Project 0.1b: Arithmetic and Simple Algebra using Maple
Objective
The objective of this project is to acquaint you with some of the arithmetic and algebraic capabilities
of Maple. Since Maple can be run on different types of computers and under different operating systems
(such as Macintosh, Windows, and UNIX), and since the choice of operating system used for this and future
projects is yours, we make minimal platform-specific comments. Questions regarding specific platforms --
including how to get Maple up and running, how to save, edit, and print -- are left to you to resolve.
Narrative
Maple combines the features of a computer algebra system with those of graphing software in one package.
In this project you will learn about some of Maple's basic algebraic features; in the next project you will
learn about some of its graphing features. To complete this project you must be able to get Maple up and
running, edit, and print.
Task
After having gotten Maple up and running, type the command lines in the left-hand column below into
Maple in the order in which they are listed. The effect of each command is described in the right-hand
column for your reference; do not type what is written in the right-hand column into Maple! Your lab report
will be a hard copy of your typed input and Maple's responses. (A summary of some basic Maple commands
for MATH 163 is available.)
> # Project 0.1b: Arithmetic and Simple Algebra Using Maple
> # This is a comment. Comments can clarify your work without affecting your computations.
> restart; Clear Maple's memory.
> 6+7; Add 6 and 7.
> 6+7: Maple performs the addition, but the colon suppresses any output.
> 9-3; Subtract 3 from 9.
> 4*3; Multiply 4 by 3.
> 24/2; Divide 24 by 2.
> 1/2+1/3; Add 1/2 and 1/3.
> evalf(%); Express the previous value as a decimal.
> Digits := 20; Henceforth express decimals to 20 places.
> evalf(%%%); Express the third-last value as a floating point number.
> 1/(2+1/3); Note that this isn't 1/2 + 1/3! The moral: watch your parentheses!
> Pi; Write .
> evalf(Pi); Write  as a decimal to 20 places.
> x := 5; Let x be 5.
> x^3; Find x3
.
> x^(1/2); Find x1/2
.
> evalf(x^(1/2)); Find (or evaluate) x1/2
as a floating point (f) number.
> x := ´x´; Reestablish x as a variable.
> x^2; Find x2
.
> 17!; Find 17!.
> p := (x-4)*(3*x+2); Let p = (x - 4)(3x + 2).
> expand(p); Expand p.
> factor(p); Factor p = 3x2
- 10x - 8.
> solve(p=0,x); Solve p = 3x2
- 10x - 8 = 0 for x exactly.
> fsolve(p=0,x); Solve p = 3x2
- 10x - 8 = 0 for x numerically.
> subs(x=5,p); Substitute 5 for x in p.
> subs(x=x+h,p); Substitute x + h for x in p.
> expand(%); Note that if we replace x + h by x in 3x2
- 10x - 8,
we don't get 3x2
- 10x - 8 + 3h2
- 10h - 8.
> expand((x+2)^8); Expand the expression (x + 2)8
.
> eqns := {x-y-z=0,6*x+4*z=12,3*y-4*z=-3}; Let eqns denote the system of equations
x - y - z = 0, 6x + 4z = 12, 3y - 4z = -3.
> sols := solve(eqns); Solve the system eqns for x, y, and z.
Comments
As you work through the projects in this and subsequent courses, think about what you're doing: think
about what you're typing, why you're typing it, and what you are -- or should be -- getting as output.
Errors often arise from simple typographical mistakes, and one of the best indicators that you've made a
typographical mistake is output that is not what it should be.