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