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Chapter 1: Brief Overview of MATLAB

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Chapter 1:Brief Overview of MATLAB

MATLAB

for Scientist and Engineers

Using Symbolic Toolbox

- Exposeyourself to the history of MATLAB,
- See what MATLAB provides,
- Look at a symbolic math example.

- 1967: "Computer solution of linear algebraic
equations", Forsythe and Moler

- 1976: "Matrix Eigensystem Routines,
EISPACK Guide" in FORTRAN

- 1976~9: "LINPACK" in FORTRAN
- 1977~: "MATLAB Environment", Cleve Moler

- 1971: "Handbook for automatic computations" in ALGOL,
- J. H. Wilkinson et. al.

Cleve Moler

(1939~)

J.H.Wilkinson, UK

(1919~1986)

- 1979: "Numerical analysis" lecture at Stanford,
- met with Jack Little, then an engineering student
- 1984: MathWorks founded by Jack and Moler

Jack Little

- Video: The Origins of MATLAB at MathWorks.com
- http://www.mathworks.com/company/aboutus/founders/clevemoler.html

- http://www.scientific-computing.com/features/feature.php?feature_id=15

- http://en.wikipedia.org/wiki/Cleve_Moler

- http://www.netlib.org/blas/

- http://en.wikipedia.org/wiki/Maple_(software)
- http://www.maplesoft.com/index1.aspx

MATLAB? Matrix Laboratory

Matrix Arithmetic, Eigen Analysis, ...

>> c=a*b

c = 32 77 80

54 62 105

64 41 100

>> d=a/b

d = 2.3934 2.0164 -2.1639

0.1475 0.1311 0.6885

5.0820 1.2951 -2.9508

>> b=floor(10*rand(3))

b = 1 5 3

6 1 8

3 6 8

>> a=magic(3)

a = 8 1 6

3 5 7

4 9 2

Graphics & Visualization

Graphical User Interface

fifteen

fdatool

Try them for yourself!

xpbombs

Toolboxes

- Model-based design environment

Ref: Help – Video and Image Processing Blockset – Demos – Motion Detection

- Math and computation
- Algorithm development
- Data acquisition
- Modeling, simulation, and prototyping
- Data analysis, exploration, and visualization
- Scientific and engineering graphics
- Application development, including graphical user interface building

Ref: Help – MATLAB – Getting Started – Introduction – Product Overview

The MATLAB system consists of these main parts:

- Desktop Tools and Development Environment
- Mathematical Function Library
- The Language
- Graphics
- External Interfaces; API
+

- Toolboxes: MATLAB function packages
- Simulink: Model-based design
- Blocksets: Simulink model packages

Ref: Help – MATLAB – Getting Started – Introduction – Product Overview

- Position of an oscillating mass:
- Velocity?

General Solution

View underlying mathematics

Ref: Webinar – Symbolic Computing Tools for Academia

Ref: Webinar – Symbolic Computing Tools for Academia

From Notebook Interface

- Conveniently manage & document symbolic computations
- Math notation, embedded text, graphics

- Access complete MuPAD language
- 15+libraries of symbolic math functions

From MATLAB

- Perform symbolic computations using familiar MATLAB syntax

Sharing

Ref: Webinar – Symbolic Computing Tools for Academia

Dynamic Equation

Initial Conditions

Symbolic Math Solution

Ref: Webinar – Symbolic Computing Tools for Academia

mass_spring_damp_system.mn

- Calculus
- Differentiation
- Integrals
- Jacobian
- Taylor series
- Limits

- Solving Equations
- Algebraic Equations
- Differential Equations

- Transforms
- Fourier transform
- Laplace transform
- Z-transform

- Simplification
- Polynomial Expansion
- Substitution

- Linear Algebra
- Operations
- Eigenvalues

- Special Functions
- Bernoulli, Bessel, Beta, …
- Fresnel sine/cosine integral, Gamma

- Variable Precision Arithmetic
- Plotting
- 2-D
- 3-D contour, surface, mesh
- Animations

Ref: Webinar – Symbolic Computing Tools for Academia