This book is intended for students who are very much interested to learn more about MATLAB and to use it for problem solving. Be it a small project or an application oriented implementation in the field of medicine, security, communication, networking etc, this book will certainly prove to be an effective source of aid to the student or academician. This book will guide students to understand about the basics of MATLAB up to deploying mathematical models in it by means of programming effectively. Examples for programming in MATLAB are included in this book so that the reader can capably practice as he surfs through the book. The reader will surely find the book useful and interesting.

We present this book with the anticipation that someone in the near future will surely be benefitted and able to continue in programming MATLAB with less toil and more passion towards his/her goal.

CONTENTS

Introduction

About this tutorial
About MATLAB
MATLAB M-Book
Getting help with MATLAB commands
Getting started with MATLAB
Vectors and matrices in MATLAB
More about M-Books
Simple graphics in MATLAB
Symbolic computation in MATLAB
Manipulating functions in MATLAB
Saving your MATLAB session
About the rest of this tutorial

Chapter 1: Classification of differential equations

Chapter 2: Models in one dimension
Section 2.1: Heat flow in a bar; Fourier's Law

Solving simple boundary value problems by integration
The MATLAB solve command

Chapter 3: Essential linear algebra
Section 3.1 Linear systems as linear operator equations
Section 3.2: Existence and uniqueness of solutions to Ax=b
Section 3.3: Basis and dimension

Symbolic linear algebra
Programming in MATLAB, part I
Defining a MATLAB function in an M-file.
Optional inputs with default values
Comments in M-files
M-files as scripts

Section 3.4: Orthogonal bases and projection

Working with the L2 inner product

Section 3.5: Eigenvalues and eigenvectors of a symmetric matrix

Numerical eigenvalues and eigenvectors
Symbolic eigenvalues and eigenvectors
Review: Functions in MATLAB

Chapter 4: Essential ordinary differential equations
Section 4.1: Solutions to some simple ODEs

Second-order linear homogeneous ODEs with constant coefficients
A special inhomogeneous second-order linear ODE
First-order linear ODEs

Section 4.2: Linear systems with constant coefficients

Inhomogeneous systems and variation of parameters
Programming in MATLAB, Part II
Conditional execution
Passing one function into another

Section 4.3: Numerical methods for initial value problems

Programming in MATLAB, part III
Efficient MATLAB programming
More about graphics in MATLAB

Chapter 5: Boundary value problems in statics
Section 5.1: Introduction to the spectral method; eigenfunctions
Section 5.2: The Galerkin method

Computing the stiffness matrix and load vector in loops

Section 5.3: Piecewise polynomials and the finite element method

Computing the load vector
Computing the stiffness matrix
The nonconstant coefficient case
Creating a piecewise linear function from the nodal values
More about sparse matrices

Chapter 6: Heat flow and diffusion
Section 6.1: Fourier series methods for the heat equation
Section 6.2: Finite element methods for the heat equation

Chapter 7: First-Order PDEs and the Method of Characteristics
Section 7.1: The simplest PDE and the method of characteristics