Differential Equations with MatLab [3rd ed.]

Description

Preface......Page 3 Contents......Page 5 Guiding Philosophy......Page 9 Student’s Guide......Page 11 Instructor’s Guide......Page 13 A Word About Software Versions......Page 14 Platforms and Versions......Page 16 Starting MatLab......Page 17 Online Help......Page 18 MatLab Windows......Page 20 Ending a Session......Page 21 Arithmetic......Page 22 Symbolic Computation......Page 23 Vectors......Page 25 Recovering from Problems......Page 26 Functions......Page 27 Managing Variables......Page 29 Solving Equations......Page 30 Graphics......Page 32 Calculus......Page 38 Some Tips and Reminders......Page 39 MatLab Desktop......Page 40 M-files......Page 43 Loops......Page 47 Presenting Your Results......Page 48 Solution to Problem Set A, Problem 2......Page 53 Debugging Your M-files......Page 54 Practice with MatLab......Page 56 Finding Symbolic Solutions......Page 60 Existence and Uniqueness......Page 63 Stability of Differential Equations......Page 65 Different Types of Symbolic Solutions......Page 68 6 MuPAD......Page 75 Direction Field for 1st Order Linear Equation......Page 81 Direction Field for Non-Linear Equation......Page 83 Autonomous Equations......Page 85 1st Order Equations......Page 91 8 Numerical Methods......Page 103 Numerical Solutions using MatLab......Page 104 Some Numerical Methods......Page 107 Controlling the Error in ode45......Page 114 Reliability of Numerical Methods......Page 115 Data Classes......Page 119 Functions and Expressions......Page 122 More about M-files......Page 123 Matrices......Page 125 Graphics......Page 127 Features of MatLab Numerical ODE Solvers......Page 130 Troubleshooting......Page 135 Constructing and Running a Simulink Model......Page 137 Output to the Workspace & how Simulink works......Page 143 Numerical Solutions......Page 146 11 Solving & Analyzing 2nd Order Linear Equations......Page 154 2nd Order Equations with MatLab......Page 156 2nd Order Equations with Simulink......Page 160 Comparison Methods......Page 162 Geometric Method......Page 165 2nd Order Equations......Page 172 12 Series Solutions......Page 186 Series Solutions......Page 188 Singular Points......Page 189 Other Linear and Nonlinear Equations......Page 191 13 Laplace Transforms......Page 193 Differential Equations & Laplace Transforms......Page 195 Discontinuous Functions......Page 198 Differential Equations with Discontinuous Forcing......Page 200 Series Solutions & Laplace Transforms......Page 203 14 Higher Order Equations & Systems of 1st Order Equations......Page 217 Higher Order Linear Equations......Page 218 Systems of First Order Equations......Page 219 Phase Portraits......Page 226 15 Qualitative Theory for Systems of DEs......Page 233 Systems of DEs......Page 240 Problem Set A, Problem 4......Page 258 Problem Set B, Problem 5......Page 259 Problem Set C, Problem 3......Page 263 Problem Set D, Problem 1......Page 266 Problem Set E, Problem 1......Page 271 Problem Set F, Problem 6......Page 274 Index......Page 282