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- Differential Equations
with Matlab
- Differential Equations
with Mathematica
- Differential Equations
with Maple
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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 M-files and M-books 31
- 4.1 The MATLAB Desktop 31
- 4.2 M-files 34
- 4.3 Loops 38
- 4.4 Presenting Your Results 38
- 4.5 Debugging Your M-files 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 Non-Linear 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 M-files 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 M-files 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
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