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. 2

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 3 J.H.Wilkinson, UK (1919~1986) Cleve Moler (1939~) Jack Little 1971: "Handbook for automatic computations" in ALGOL, J. H. Wilkinson et. al. 1979: "Numerical analysis" lecture at Stanford, met with Jack Little, then an engineering student 1984: MathWorks founded by Jack and Moler

Further Digging Resources Video: The Origins of MATLAB at MathWorks.com Meet Mr Matlab at Scientific Computing World Cleve Moler at Wikipedia BLAS at Netlib.org Maple at Wikipedia and Maplesoft.com 4

MATLAB? Matrix Laboratory >> b=floor(10*rand(3)) b = >> a=magic(3) a = >> b=floor(10*rand(3)) b = >> a=magic(3) a = >> c=a*b c = >> d=a/b d = >> c=a*b c = >> d=a/b d = Matrix Arithmetic, Eigen Analysis,... 5

Graphics & Visualization 6

Graphical User Interface Try them for yourself! 7 xpbombs fifteen fdatool

Toolboxes 8

SIMULINK Model-based design environment 9 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 10 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 Simulink: Model-based design Blocksets: Simulink model packages 11 Ref: Help – MATLAB – Getting Started – Introduction – Product Overview

What is Symbolic Computing Position of an oscillating mass: Velocity? 12 General Solution View underlying mathematics Ref: Webinar – Symbolic Computing Tools for Academia

Symbolic Math Usage in Academia 13 Ref: Webinar – Symbolic Computing Tools for Academia

Working w/t Symbolic Math Toolbox From MATLAB Perform symbolic computations using familiar MATLAB syntax 14 From Notebook Interface Conveniently manage & document symbolic computations Math notation, embedded text, graphics Access complete MuPAD language 15+libraries of symbolic math functions Sharing Ref: Webinar – Symbolic Computing Tools for Academia

Dynamic Equation Initial Conditions Symbolic Math Solution Demo: Mass-Spring-Damp System 15 mass_spring_damp_system.mn Ref: Webinar – Symbolic Computing Tools for Academia

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 16 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