WILEY. Differential Equations with MATLAB (Third Edition) Brian R. Hunt Ronald L. Lipsman John E. Osborn Jonathan M. Rosenberg
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1 Differential Equations with MATLAB (Third Edition) Updated for MATLAB 2011b (7.13), Simulink 7.8, and Symbolic Math Toolbox 5.7 Brian R. Hunt Ronald L. Lipsman John E. Osborn Jonathan M. Rosenberg All of the University of Maryland, College Park WILEY John Wiley & Sons, Inc. New York Chichester Weinheim Brisbane Singapore Toronto in
2 Contents Preface v 1 Introduction Guiding Philosophy Student's Guide Instructor's Guide MATLAB, MuPAD, and Simulink ODE Chapters Computer Problem Sets A Word About Software Versions 6 2 Getting Started with MATLAB Platforms and Versions Installation Starting MATLAB Typing in the Command Window Online Help MATLAB Windows Ending a Session 14 3 Doing Mathematics with MATLAB Arithmetic Symbolic Computation Substituting in Symbolic Expressions Symbolic Expressions and Variable Precision Arithmetic Vectors Suppressing Output Recovering from Problems Errors in Input Aborting Calculations Functions Built-in Functions User-defined Functions Managing Variables 22 Vll
3 viii Contents 3.7 Solving Equations Graphics Graphing with ezplot Modifying Graphs Graphing with plot Plotting Multiple Curves Parametric Plots Implicit Plots and Contour Plots Calculus Some Tips and Reminders 32 4 Using the Desktop and M-files The MATLAB Desktop The Workspace The Current Folder and Search Path The Command History M-files Script M-files Function M-files Cells Loops Presenting Your Results Presenting Graphics Pretty Printing "Publishing" an M-file M-books Preparing Homework Solutions Debugging Your M-files 47 Problem Set A: Practice with MATLAB 49 5 Solutions of Differential Equations Finding Symbolic Solutions Existence and Uniqueness Stability of Differential Equations Different Types of Symbolic Solutions 61 6 MuPAD 69 7 A Qualitative Approach to Differential Equations Direction Field for a First Order Linear Equation Direction Field for a Non-Linear Equation Autonomous Equations Examples of Autonomous Equations 81
4 Contents ix Problem Set B: First Order Equations 85 8 Numerical Methods Numerical Solutions Using MATLAB Some Numerical Methods The Euler Method The Improved Euler Method The Runge-Kutta Method Inside ode Round-off Error Controlling the Error in ode Reliability of Numerical Methods Features of MATLAB Data Classes String Manipulation Symbolic and Floating Point Numbers Structures Functions and Expressions More about M-files Variables in Script M-files Variables in Function M-files Structure of Function M-files Matrices Solving Linear Systems Calculating Eigenvalues and Eigenvectors Graphics Figure Windows Editing Figures Features ofmatlab's Numerical ODE Solvers Evaluation of Numerical Solutions with deval Plotting Families of Numerical Solutions of ODEs Event Detection Troubleshooting The Most Common Mistakes Error and Warning Messages Using Simulink Constructing and Running a Simulink Model Output to the Workspace and How Simulink Works 137 Problem Set C: Numerical Solutions 141
5 x Contents 11 Solving and Analyzing Second Order Linear Equations Second Order Equations with MATLAB Second Order Equations with Simulink Comparison Methods The Interlacing of Zeros Proof of the Sturm Comparison Theorem A Geometric Method The Constant Coefficient Case The Variable Coefficient Case Airy's Equation Bessel's Equation Other Equations 165 Problem Set D: Second Order Equations Series Solutions Series Solutions Singular Points Other Linear and Nonlinear Equations Laplace Transforms Differential Equations and Laplace Transforms Discontinuous Functions Differential Equations with Discontinuous Forcing 194 Problem Set E: Series Solutions and Laplace Transforms Higher Order Equations and Systems of First Order Equations Higher Order Linear Equations Systems of First Order Equations Linear First Order Systems Using MATLAB to Find Eigenpairs Phase Portraits Plotting a Single Trajectory Plotting Several Trajectories Numerical Solutions of First Order Systems A Non-Linear System Qualitative Theory for Systems of Differential Equations 227 Problem Set F: Systems of Differential Equations 235 Sample Solutions 253 Index 277
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