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 Differential Equations
with Matlab
 Differential Equations
with Mathematica
 Differential Equations
with Maple

Differential Equations with MATLAB, 2nd Edition
Table of Contents
 Preface iii
 1 Introduction 1
 1.1 Guiding Philosophy 1
 1.2 Student's Guide 3
 1.3 Instructor's Guide 4
 1.4 A Word About Software Versions 6
 2 Getting Started with MATLAB 7
 2.1 Platforms and Versions 7
 2.2 Installation 8
 2.3 Starting MATLAB 8
 2.4 Typing in the Command Window 9
 2.5 Online Help 9
 2.6 MATLAB Windows 11
 2.7 Ending a Session 12
 3 Doing Mathematics with MATLAB 13
 3.1 Arithmetic 13
 3.2 Recovering from Problems 14
 3.3 Symbolic Computation 15
 3.4 Vectors 17
 3.5 Functions 18
 3.6 Managing Variables 20
 3.7 Solving Equations 21
 3.8 Graphics 23
 3.9 Calculus 29
 3.10 Some Tips and Reminders 30
 4 Using Mfiles and Mbooks 31
 4.1 The MATLAB Desktop 31
 4.2 Mfiles 34
 4.3 Loops 38
 4.4 Presenting Your Results 38
 4.5 Debugging Your Mfiles 45
 Problem Set A: Practice with MATLAB 47
 5 Solutions of Differential Equations 51
 5.1 Finding Symbolic Solutions 51
 5.2 Existence and Uniqueness 54
 5.3 Stability of Differential Equations 55
 5.4 Different Types of Symbolic Solutions 59
 6 A Qualitative Approach to Differential Equations 65
 6.1 Direction Field for a First Order Linear Equation 65
 6.2 Direction Field for a NonLinear Equation 68
 6.3 Autonomous Equations 69
 Problem Set B: First Order Equations 75
 7 Numerical Methods 87
 7.1 Numerical Solutions Using MATLAB 88
 7.2 Some Numerical Methods 91
 7.3 Controlling the Error in ode45 98
 7.4 Reliability of Numerical Methods 99
 8 Features of MATLAB 103
 8.1 Data Classes 103
 8.2 Functions and Expressions 106
 8.3 More about Mfiles 107
 8.4 Matrices 109
 8.5 Graphics 111
 8.6 Features of MATLAB 's Numerical ODE Solvers 114
 8.7 Troubleshooting 119
 9 Using Simulink 121
 9.1 Constructing and Running a Simulink Model 121
 9.2 Output to the Workspace and How Simulink Works 127
 Problem Set C: Numerical Solutions 131
 10 Solving and Analyzing Second Order Linear Equations 139
 10.1 Second Order Equations with MATLAB 141
 10.2 Second Order Equations with Simulink 145
 10.3 Comparison Methods 147
 10.4 A Geometric Method 150
 Problem Set D: Second Order Equations 157
 11 Series Solutions 171
 11.1 Series Solutions 172
 11.2 Singular Points 174
 11.3 Function Mfiles for Series Solutions 177
 11.4 Series Solutions Using maple 180
 12 Laplace Transforms 183
 12.1 Differential Equations and Laplace Transforms 185
 12.2 Discontinuous Functions 188
 12.3 Differential Equations with Discontinuous Forcing 190
 Problem Set E: Series Solutions and Laplace Transforms 193
 13 Higher Order Equations and Systems of First Order Equations 207
 13.1 Higher Order Linear Equations 208
 13.2 Systems of First Order Equations 209
 13.3 Phase Portraits 216
 14 Qualitative Theory for Systems of Differential Equations 223
 Problem Set F: Systems of Differential Equations 231
 Glossary 247
 Sample Solutions 259
 Index 285
