Chapter 2:
First Steps in MuPAD
MATLAB for Scientist and Engineers
Using Symbolic Toolbox
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You are going to See the difference between numerical com-
puting 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
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Numerical Computations
Problem solving by number calculations Approximate solutions as fast as possible Numbers are stored by floating-point repre-
sentation. The only way when no closed form solution
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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 simplify-
ing the expressions.
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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
Ref: http://en.wikipedia.org/wiki/MuPAD
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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/
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Starting MuPAD
Two ways of starting MuPAD1. Type mupad in the command window.
2. Start button
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MuPAD Notebook
>> mupadFormat Toolbar
Standard Toolbar
Output Region
Command Bar
Menu Bar
Input Region
Ctr-I
Text Region
Ctr-T
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Working with Input Regions
Enter
EnterShift +Enter
Enter
Evaluate and show the results.
Evaluate but do notshow the results.
The expressionscontinues to the next line
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Evaluation after Modification
Once you change the value of variable, you can re-evaluate the other dependent expressions.
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Accessing Help
Completing Commands:
Tool Tips: mouse over the command
SpaceCtrl +
Complete Help: right mouse click
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Computing Numbers
real number!Assignment!
Convert toa real number!
Change precision.
delete DIGITS PI E
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Complex Numbers1 i
imaginary
real
magnitude
in radian
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Differentiation
df
dx
2
2
df
dx
2
2
df
dx
df
da
d df
da dx
D(f) f'
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Integration
2cos( )x dx
4 2
0cos( )x dx
No closed form solution !
Numeric integration
2xe dx
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Solving Equations
solve
Solve Algebraic Equations
Solve Ordinary Differential Equations
Solve Inequalities
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Graphics
2-D Function Plotting
2-D Animation
3-D Function Plotting
3-D Animation
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Manipulating Expressions
Simplifying the expressions
Factoring, Expanding, Collecting, and etc.
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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
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Creating 2-D Plots Set range.
Parameter assignment.
Sequence of plots.
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Creating 2-D Plots (cont.)
Multiple Plots Piecewise Functions
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Creating 3-D Plots
Three Dim.
Sequence of 3D Plots
Animation Control
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Animated 2-D Plots
Additional parameter isregarded as the animationparameter.
2-D point
2-D curve
Animationparameter
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Animated 3-D Plots
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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 ani-
mations
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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+
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Notes
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Notes