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Chapter 1: Brief Overview of MATLAB. MATLAB for Scientist and Engineers Using Symbolic Toolbox. You are going to. Expose yourself to the history of MATLAB, See what MATLAB provides, Look at a symbolic math example. Old History of MATLAB. 1967: "Computer solution of linear algebraic

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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

### You are going to

• Exposeyourself to the history of MATLAB,

• See what MATLAB provides,

• Look at a symbolic math example.

### Old History of MATLAB

• 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

### Further Digging Resources

• Video: The Origins of MATLAB at MathWorks.com

• Meet MrMatlab at Scientific Computing World

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

• Cleve Moler at Wikipedia

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

• BLAS at Netlib.org

• http://www.netlib.org/blas/

• Maple at Wikipedia and Maplesoft.com

• 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

### They Use MATLAB for …

• 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

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

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

### What is Symbolic Computing

• Position of an oscillating mass:

• Velocity?

General Solution

View underlying mathematics

Ref: Webinar – Symbolic Computing Tools for Academia

### Symbolic Math Usage in Academia

Ref: Webinar – Symbolic Computing Tools for Academia

### Working w/t Symbolic Math Toolbox

From Notebook Interface

• Conveniently manage & document symbolic computations

• Math notation, embedded text, graphics

• 15+libraries of symbolic math functions

From MATLAB

• Perform symbolic computations using familiar MATLAB syntax

Sharing

Ref: Webinar – Symbolic Computing Tools for Academia

### Demo: Mass-Spring-Damp System

Dynamic Equation

Initial Conditions

Symbolic Math Solution

Ref: Webinar – Symbolic Computing Tools for Academia

mass_spring_damp_system.mn

### Symbolic Math Toolbox Libraries

• 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