First Steps in MuPAD

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21 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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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