# First Steps in MuPAD

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Nov 21, 2013 (4 years and 6 months ago)

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Chapter 2:

First Steps in MuPAD

MATLAB

for Scientist and Engineers

Using Symbolic Toolbox

You are going to

See

the difference between numerical
computing and symbolic computing

Say

hello to
MuPAD

notebook

Enjoy

the kind help system of
MuPAD

Taste

the sweet power of symbolic computing

Create

basic 2
-
D, 3
-
D graphs and animations

Be

glad

to know that
MuPAD

is there for you

2

Numerical Computations

Problem solving by
number

calculations

Approximate solutions
as fast as possible

Numbers are stored by
floating
-
point

representation.

The only way
when no closed form solution

3

Computer Algebra

Problem solving by
symbolic

computations

Exact solution
as fast as possible

Numbers are stored by
integer

fractions.

Requires
more computing
power and storage

Can help numerical computation by
simplifying the expressions.

4

MuPAD Software

Originally developed
by the MuPAD research group at the
University of Paderborn
, Germany.

A
computer algebra system

to manipulate formulas
symbolically

Program packages for
linear algebra
,
differential equations
,
number theory
,
statistics
,
functional programming

An interactive graphic system that supports animations and
transparent areas in 3D

Classic and verified
numerical analysis

in discretionary
accuracy

A
programming language

that supports
object orientation

and
functional programming

5

Ref: http://en.wikipedia.org/wiki/MuPAD

Other Options

Mathematica
,
www.wolfram.com

Maple,
www.maplesoft.com

IDL,
www.ittvis.com/ProductServices/IDL.aspx

,
www.gnu.org/software/octave/

M ,
www.ptc.com/products/mathcad/

Ref:
http://amath.colorado.edu/computing/mmm/

6

Starting MuPAD

Two ways of starting MuPAD

1.
Type
mupad

in the command window.

2.
Start button

7

MuPAD Notebook

>>
mupad

8

Format Toolbar

Standard Toolbar

Output Region

Command Bar

Menu Bar

Input Region

Ctr
-
I

Text Region

Ctr
-
T

Working with Input Regions

9

Enter

Enter

Shift

+

Enter

Enter

Evaluate and

show the results.

Evaluate but
do not

show

the results.

Th
e expressions

continues to

the next line

Evaluation after Modification

Once you change the value of variable, you can
re
-
evaluate the other dependent expressions.

10

Accessing Help

Completing Commands:

Tool Tips:

mouse over the command

11

Space

Ctrl

+

Complete

Help
:

right mouse click

Computing Numbers

12

real number!

Assignment!

Convert to

a
real number!

Change

precision.

delete DIGITS

PI

E

Complex Numbers

13

1
i
 
imaginary

real

magnitude

in radian

Differentiation

14

d
f
dx
2
2
d
f
dx
2
2
d
f
dx
d
f
da
d d
f
da dx
D(f)

f'

Integration

15

2
cos( )
x dx

4
2
0
cos( )
x dx

No

closed form

solution !

Numeric integration

2
x
e dx



Solving Equations

solve

16

Solve Algebraic Equations

Solve Ordinary Differential Equations

Solve Inequalities

Graphics

2
-
D Function Plotting

2
-
D Animation

3
-
D Function Plotting

3
-
D Animation

17

Manipulating Expressions

Simplifying the expressions

Factoring, Expanding, Collecting, and etc.

18

Basic Plotting Options

With
plot

command, you can

Create 2
-
D and 3
-
D function plots

Specify plotting range

Create plots for piecewise functions

Create multiple function plots in one graph

Create animated 2
-
D and 3
-
D function plots

19

Creating 2
-
D Plots

20

Set range.

Parameter

assignment.

Sequence

of plots.

Creating 2
-
D Plots (cont.)

21

Mul
tiple Plots

Piecewise Functions

Creating 3
-
D Plots

22

Three Dim.

Sequence of

3D Plots

Animation Control

Animated 2
-
D Plots

23

Additional parameter is

regarded as the animation

parameter.

2
-
D

point

2
-
D

curve

Animation

parameter

Animated 3
-
D Plots

24

Key Takeaways

Now, you are able to

tell the differences between numerical computing
and symbolic computing,

expand your knowledge on
MuPAD

by yourself
using
MuPAD

help system,

apply differentiation, indefinite integrals, definite
integrals on math expressions and functions,

solve an equation or a set of equations,

manipulate math expressions at your will,

and to create basic 2
-
D and 3
-
D graphs and
animations

25

MuPAD

Commands Review

26

mupad

:=

:

float

PI

E

abs

rectform

Re

Im

arg

conjugate

diff

int

infinity

assuming

solve

factor

expand

simplify

collect

partfrac

ode

Simplify

Shift

Enter

+

Ctr

Space

+

Ctr

T

+

Ctr

I

+

Notes

27

Notes

28