Maple

Maple

Don't worry about your difficulties in Mathematics. I

can assure you mine are still greater.

~Albert Einstein

Mathematics touches us every day—from the simple

chore of calculating the total cost of our purchases to

the complex calculations used to construct the bridges

we travel.

Azat AzhibekovDepartment of Computer Education & Instructional Technologies

Fatih University,34500 Büyükçekmece,Istanbul, Turkey

E-mail:[email protected]

Overview

What is Maple?

Why do I need Maple?

How can I use Maple?

1Maple

Learning Objectives

Introduction to Maple

Getting started

Learning basic syntax

Using Maple as a calculator

2Maple

1. Introduction to Maple

Maple is a commercial computer algebra

system developed and sold commercially

by Maplesoft, a software company based

in Waterloo, Ontario, Canada,www.maplesoft.com

It is a very powerful interactive computer algebra

system for doing maths and used by students,

educators, mathematicians, statisticians, scientists,

and engineers for doing numerical and symbolic

computation.

Maple is available on Windows, Macintosh, UNIX,

and Linux systems.

Maple 3

http://en.wikipedia.org/wiki/Computer_algebra_system

http://en.wikipedia.org/wiki/Computer_algebra_system

http://en.wikipedia.org/wiki/Maplesoft

http://en.wikipedia.org/wiki/Waterloo,_Ontario

http://en.wikipedia.org/wiki/Canada

1.2 Strengths

Maple has many strengths:

1) Exact integer computation

2) Numerical computation to any (well, almost) number of

specified digits

3) Symbolic computation

4) Many built-in functions and packages for doing a wide variety of

mathematical tasks

5) Facilities for doing two- and three-dimensional plotting and

animation

6) A worksheet-based interface

7) Facilities for making technical documents

8) Maple is a simple programming language, which means that

users can easily write their own functions and packages.

Maple 4

2. Getting Started

On most systems a maple session is started by double

clicking on the maple icon . In the UNIX X Windows version,

maple is started by entering the command xmaple.

After starting, you'll have two choices: document mode and

worksheet mode. Select Worksheet mode to bring up an edit

window with a > character and a blinking cursor.

Maple commands are entered to the right of the > character.

Press Enter to see results

You can also get Maple to return the result on the same line

as your question by typing [Ctrl][=] (hold down the control key,

then press the = key).

5Maple

2.1 Standard (default) Interface

In most

versions Menu

bar appears at

the top of the

window.

Below Menu

bar there is

Tool bar with 27

buttons

Beneath is

Context bar

with 5 buttons

Palettes on the

left

6Maple

Fig.1

2.1 Document Mode

7

• You can create

powerful interactive

documents. You can

visualize and animate

problems in two and

three dimensions. You

can solve complex

problems with simple

point-and-click

interfaces or easy-to

modify interactive

documents. While you

work, you can

document your

process, providing text

descriptions.Fig.2

Maple

2.2 Worksheet Mode

8Maple

• In worksheet

mode(Fig.3) we

have [> character.

• Commands are

entered to the right

of the [> character

• Except [> character,

everything is similar

to Fig.2

Fig.3

2.3 Classic Interface

A basic worksheet environment for older

computers with limited memory. The

Classic interface does not offer all of the

graphical user interface features that are

available in the Standard interface. The

Classic interface has only one mode,

Worksheet mode.

9Maple

2.4 Command-line Version

Interface

Command-line interface for solving very

large complex problems or batch

processing with scripts. No graphical

user interface features are available

10Maple

2.5 Maplet Applications

Graphical user interfaces containing

windows, textbox regions, and other

visual interfaces, which gives you point-

and-click access to the power of Maple.

You can perform calculations and plot

functions without using the worksheet.

11Maple

2.6 Maplesoft Graphing

Calculator

A graphical calculator interface to the

Maple computational engine. Using it,

you can perform simple computations

and create customizable, zoomable

graphs. This is available on Microsoft®

Windows® only.

12Maple

2.7 Context Menu

A context menu is a popup menu that lists the operations and

actions you can perform on a particular expression.

Fig.4

13Maple

3. Basic Syntax

1. Assignment of a name or variable to a mathematical object

is done using the := assignment operator

2. Each instruction to Maple must end with a colon (:) or a semi-

colon (;). If the colon is used, the command is executed but

the output is not printed. When the semicolon is used, the

output is printed.

3. Maple input is case-sensitive; x is not the same as X in

Maple

4. The pound sign (#) is used to indicate comments. Everything

following the # sign to the end of the line is ignored

5. Maple provides extensive online help. To obtain help, enter ?

followed by the subject for which help is needed, e.g.,

?integration. It is the only command that doesn't with : or ;

14Maple

3. Basic Syntax (continued)

6. Variables remain assigned to whatever value or

expression that they were last assigned until and unless

they are reassigned or cleared. To determine the current

assignment of a variable, enter its name followed by a

semi-colon;

7. The % command can be used a shorthand expression to

represent the result of the previous command.

8. = is used for writing equations

9. Enter restart; to clear all previously assigned variables

15Maple

3.1 Maple as a Calculator

In its simplest form, Maple can serve as a calculator. It

even provides a convert function for unit conversions.

For example, to enter a diameter of 3 ft and calculate

the area in m2, enter the following commands.

16Maple

(3.1)

3.2 Basic Functions

17Maple

Function Meaning

abs(x) absolute value lxl

sqrt(x) square root √x

n! factorial

sin(x) sine

cos(x) cosine

tan(x) tangent

sec(x) secant

csc(x) cosecant

cot(x) cotangent

log(x)also ln(x)

natural logarithm

exp(x) exponential function

sinh(x) hyperbolic sine

cosh(x) hyperbolic cosine

tanh(x) hyperbolic tan

Operation Meaning

+ addition

- subtraction

* multiplication

/ division

^ exponentiation

Table 1

Table 2

• For complete list of Functions,

see ?index[functions]

(3.2)

3.3 Entering Math

There are a number of methods to enter math into Maple. You

can enter math using a combination of palettes, keyboard

shortcuts, context menus and commands. Most operations

can be entered in more than one way, so you can pick the

method you are most comfortable with.

Palettes:

Maple has over 1000 palette symbols within the 20 palette

menus. You can also use Maple's expression palette to input

data. The expression palette contains fill-in-the-blank

templates for common operations.

Maple 18

3.4 Evaluating Expression and

Solving Equation

Equation types:

19Maple

Equation Type Solution Method

Equations and inequalities solve & fsolve commands

Ordinary differential equations ODE Analyser Assistant(dsolve) command

Partial differential equations pdsolve command

Integer equations isolve command

Integer equations in finite field msolve command

Linear integer equaions intsolve command

Linear sysytems Linear Algebra[linear solve]command

Recurrence relations rsolve command

Table 3


Solving Equation (continued)

One of the most useful capabilities of Maple is its ability to

analytically solve algebraic equations in symbolic form. This

capability will be demonstrated by solving a quadratic equation, y = a

x2 + b x + c . First, specify the equation y.

The values of a, b, and c, as well as x, are not yet specified. We can

evaluate y at specific values of these parameters using the eval

command; the first argument of the eval command is the expression

while the second is the substitution. For example, to obtain a

symbolic expression for y evaluated at x=1:

20Maple

(3.4.1)

(3.4.2)


Solving Equation (continued)

The evaluation can occur with multiple substitutions

by specifying the values of more than one variable;

in this case, the list of specifications must be

enclosed in curly braces and separated by

commas. The value of y at x = 1, a = -2, b = 3, and

c = 4 is obtained according to:

21Maple

(3.4.3)


Solving Equation(continued)

22Maple

Maple can solve an equation using the solve command. The first

argument of the solve command is the equation to be solved

while the second is the variable that should be solved for. For

example, the value(s) of x that satisfies the equation y = -2 can

be determined using the solve command, as shown below. The

result of the solve command is placed in variable xs. a, b and c

have not been assigned to values at this point, so it is necessary

to tell Maple which of the unspecified variables we wish to solve

for, x in this case, and the solution will be expressed symbolically

in terms of the remaining variables.

(3.4.4)



There are two solutions to the quadratic equation and Maple

has identified both. The variable xs contains both solutions in

two elements, xs[1] and xs[2]:

23Maple

(3.4.5)



We can set values for a, b, and c and then determine the

numerical, as opposed to symbolic, solutions to the equation.

Maple displays results in analytical form when it can; using the

evalf function results in the value being displayed in floating point

format

24Maple

(3.4.6)

(3.4.7)

3.5 Floating Point Arithmetic

25Maple

Maple can do floating-point calculation to any required precision.

This is done using evalf

(3.5)

3.5 Floating Point Arithmetic

(continued)

Notice that evalf found tan(π/5),Pi to 10 decimal places, which is the

default. Also, note that in maple, π is represented by Pi. You can

request more for one specific computation through evalf or if you

change the value of the global variable Digits to tell Maple how

many digits to use normally.

Maple 26

(3.5.1)

3.6 Substitution and

Simplification

The ability to symbolically manipulate equations provided by

Maple is extensive. It is further enhanced by the subs

(substitute) command that can be used to substitute a numerical

value or symbolic expression in place of a variable. For example,

suppose that you know that

and you wish to apply a coordinate transformation for which

Maple 27

(3.6)

(3.6.1)


Simplification (continued)

Enter the equation into Maple and apply the subs command for the

transformation.

Note that the result provided by Maple can often be expressed in an

equivalent but algebraically simpler manner by using the simplify

command.

Maple 28

(3.6.2)

(3.6.3)


Simplification (continued)

The subs command can also be used to substitute numerical values

for a variable. For example

The eval command provides the same result:

The subs and eval commands have overlapping capability.

Maple 29

(3.5.4)

(3.5.5)

4. System Requirements

Maple 30


(continued)

31Maple


(continued)

32Maple

Conclusion

Maple is a very powerful program and

can be used in scientific purposes

By using Maple we can engage

ourselves and others in learning Math

If we know commands,functions and

menus,we will enjoy our student life

All other things you need to know will

come by time

33Maple

Thank you!!!