Chapter 2:
First Steps in MuPAD
MATLAB
for Scientist and Engineers
Using Symbolic Toolbox
You are going to
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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
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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
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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
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Originally developed by the MuPAD research group at the
University of Paderborn, Germany.
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A computer algebra system to manipulate formulas
symbolically
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Program packages for linear algebra, differential equations,
number theory, statistics, functional programming
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An interactive graphic system that supports animations and
transparent areas in 3D
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Classic and verified numerical analysis in discretionary
accuracy
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A programming language that supports object orientation and
functional programming
Ref: http://en.wikipedia.org/wiki/MuPAD
5
Other Options
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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
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Two ways of starting MuPAD
1.
Type mupad in the command window.
2.
Start button
7
MuPAD Notebook
>> mupad
Format Toolbar
Menu Bar
Command Bar
Text Region
Ctr-T
Input Region
Ctr-I
Output Region
Standard Toolbar
8
Working with Input Regions
Evaluate and
show the results.
Enter
Evaluate but do not
show the results.
Enter
Shift
+
Enter
Enter
The expressions
continues to
the next line
9
Evaluation after Modification
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Once you change the value of variable, you can
re-evaluate the other dependent expressions.
10
Accessing Help
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Completing Commands:
Ctrl

+
Space
Tool Tips:
mouse over the command
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Complete Help:
right mouse click
11
Computing Numbers
Assignment!
real number!
Change
precision.
Convert to
a real number!
delete DIGITS
PI
E
12
Complex Numbers
1  i
magnitude
imaginary
real
in radian
13
Differentiation
d
f
dx
d2
f
2
dx
d
f
da
d d
f
da dx
d2
f
2
dx
D(f)
f'
14
Integration



e
 x2
dx
2
cos(
x
)
dx


 4
0
No closed form
solution !
cos( x)2 dx
Numeric integration
15
Solving Equations
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solve
Solve Algebraic Equations
Solve Inequalities
Solve Ordinary Differential Equations
16
Graphics
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2-D Function Plotting
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2-D Animation
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3-D Function Plotting
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3-D Animation
17
Manipulating Expressions
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Simplifying the expressions
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Factoring, Expanding, Collecting, and etc.
18
Basic Plotting Options
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With plot command, you can
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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
Parameter
assignment.
Set range.
Sequence
of plots.
20
Creating 2-D Plots (cont.)
Multiple Plots
Piecewise Functions
21
Creating 3-D Plots
Animation Control
Three Dim.
Sequence of
3D Plots
22
Animated 2-D Plots
2-D point
Animation
parameter
Additional parameter is
regarded as the animation
parameter.
2-D curve
23
Animated 3-D Plots
24
Key Takeaways
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Now, you are able to
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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
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
26
Notes
27
Notes
28