- Preface iii
- 1 Introduction 1
- 1.1 Guiding Philosophy 1
- 1.2 Student's Guide 3
- 1.3 Instructor's Guide 5
- 1.4 A Word About Software Versions 6
- 2 Getting Started with MATLAB 9
- 2.1 Platforms and Versions 9
- 2.2 Installation 10
- 2.3 Starting MATLAB 10
- 2.4 Typing in the Command Window 11
- 2.5 Online Help 11
- 2.6 MATLAB Windows 13
- 2.7 Ending a Session 14
- 3 Doing Mathematics with MATLAB 15
- 3.1 Arithmetic 15
- 3.2 Symbolic Computation 16
- 3.3 Vectors 18
- 3.4 Recovering from Problems 19
- 3.5 Functions 20
- 3.6 Managing Variables 22
- 3.7 Solving Equations 23
- 3.8 Graphics 25
- 3.9 Calculus 31
- 3.10 Some Tips and Reminders 32
- 4 Using the Desktop and M-files 33
- 4.1 The MATLAB Desktop 33
- 4.2 M-files 36
- 4.3 Loops 40
- 4.4 Presenting Your Results 41
- 4.5 Debugging Your M-files 47
- Problem Set A: Practice with MATLAB 47
- 5 Solutions of Differential Equations 53
- 5.1 Finding Symbolic Solutions 53
- 5.2 Existence and Uniqueness 56
- 5.3 Stability of Differential Equations 58
- 5.4 Different Types of Symbolic Solutions 61
- 6 MuPAD 69
- 7 A Qualitative Approach to Differential Equations 75
- 7.1 Direction Field for a First Order Linear Equation 75
- 7.2 Direction Field for a Non-Linear Equation 77
- 7.3 Autonomous Equations 79
- Problem Set B: First Order Equations 85
- 8 Numerical Methods 97
- 8.1 Numerical Solutions Using MATLAB 98
- 8.2 Some Numerical Methods 101
- 8.3 Controlling the Error in ode45 108
- 8.4 Reliability of Numerical Methods 109
- 9 Features of MATLAB 113
- 9.1 Data Classes 113
- 9.2 Functions and Expressions 116
- 9.3 More about M-files 117
- 9.4 Matrices 119
- 9.5 Graphics 121
- 9.6 Features of MATLAB's Numerical ODE Solvers 124
- 9.7 Troubleshooting 129
- 10 Using Simulink 131
- 10.1 Constructing and Running a Simulink Model 131
- 10.2 Output to the Workspace and How Simulink Works 137
- Problem Set C: Numerical Solutions 141
- 11 Solving and Analyzing Second Order Linear Equations 149
- 11.1 Second Order Equations with MATLAB 151
- 11.2 Second Order Equations with Simulink 155
- 11.3 Comparison Methods 157
- 11.4 A Geometric Method 160
- Problem Set D: Second Order Equations 167
- 12 Series Solutions 181
- 12.1 Series Solutions 182
- 12.2 Singular Points 183
- 12.3 Other Linear and Nonlinear Equations 185
- 13 Laplace Transforms 187
- 13.1 Differential Equations and Laplace Transforms 189
- 13.2 Discontinuous Functions 192
- 13.3 Differential Equations with Discontinuous Forcing 194
- Problem Set E: Series Solutions and Laplace Transforms 197
- 14 Higher Order Equations and Systems of First Order Equations 211
- 14.1 Higher Order Linear Equations 212
- 14.2 Systems of First Order Equations 213
- 14.3 Phase Portraits 220
- 15 Qualitative Theory for Systems of Differential Equations 227
- Problem Set F: Systems of Differential Equations 235
- Sample Solutions 253
- Index 277