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
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