Preface | p. iii |
Introduction | p. 1 |
Guiding Philosophy | p. 1 |
Student's Guide | p. 3 |
Instructor's Guide | p. 4 |
Maple | p. 4 |
ODE Chapters | p. 5 |
Computer Problem Sets | p. 5 |
A Word about Software Versions | p. 6 |
Getting Started with Maple | p. 7 |
Platforms and Versions | p. 7 |
Installation | p. 7 |
Starting Maple | p. 8 |
Maple Input | p. 8 |
Online Help | p. 9 |
Ending a Session | p. 9 |
Doing Mathematics with Maple | p. 11 |
Arithmetic | p. 11 |
Symbolic Computation | p. 12 |
Assignments | p. 13 |
Working with Output | p. 14 |
Recovering from Problems | p. 15 |
Errors in Input | p. 15 |
Aborting Calculations | p. 15 |
Suppressing Output | p. 16 |
The Restart Command | p. 16 |
Equations | p. 16 |
Solving Equations | p. 17 |
Functions and Expressions | p. 19 |
Built-in Functions | p. 19 |
User-defined Functions | p. 20 |
Expressions | p. 21 |
Substitution | p. 22 |
Sequences, Sets, and Lists | p. 23 |
Packages | p. 24 |
Graphics | p. 25 |
Plotting Functions and Expressions | p. 25 |
Plotting Multiple Curves | p. 26 |
Plotting Points | p. 27 |
Adding Text to a Plot | p. 27 |
Parametric Plots | p. 29 |
Implicit Plots | p. 30 |
Contour Plots | p. 30 |
Calculus | p. 31 |
More on Sequences, Lists, and Sets | p. 34 |
Procedures | p. 37 |
Some Tips and Reminders | p. 39 |
Using Maple Documents | p. 41 |
The Maple Window | p. 41 |
Organization of a Document | p. 42 |
Document Blocks | p. 42 |
Graphics | p. 43 |
Preparing Homework Solutions | p. 44 |
Practice with Maple | p. 47 |
Solutions of Differential Equations | p. 51 |
Finding Symbolic Solutions | p. 51 |
Existence and Uniqueness | p. 53 |
Stability of Differential Equations | p. 55 |
Different Types of Symbolic Solutions | p. 59 |
A Qualitative Approach to Differential Equations | p. 65 |
Direction Field for a First Order Linear Equation | p. 65 |
Direction Field for a Non-Linear Equation | p. 67 |
Autonomous Equations | p. 68 |
Examples of Autonomous Equations | p. 70 |
First Order Equations | p. 73 |
Numerical Methods | p. 83 |
Numerical Solutions Using Maple | p. 84 |
Some Numerical Methods | p. 86 |
The Euler Method | p. 86 |
The Improved Euler Method | p. 89 |
The Runge-Kutta Method | p. 90 |
Inside dsolve(..., numeric) | p. 91 |
Round-off Error | p. 91 |
Controlling the Error in dsolve(..., numeric) | p. 92 |
Reliability of Numerical Methods | p. 92 |
Features of Maple | p. 97 |
Names and Values | p. 97 |
Clearing Values | p. 98 |
Vectors and Matrices | p. 98 |
Solving Linear Systems | p. 100 |
Calculating Eigenvalues and Eigenvectors | p. 101 |
Plots for ODEs | p. 102 |
Commands for Plotting Direction Fields | p. 102 |
Plotting Families of Numerical Solutions of ODEs | p. 102 |
More about D Eplot | p. 103 |
Stopping Conditions | p. 105 |
Numerical Solutions of Higher Order Differential Equations | p. 106 |
Troubleshooting | p. 107 |
The Common Mistakes | p. 108 |
Error and Warning Messages | p. 108 |
Numerical Solutions | p. 111 |
Solving and Analyzing Second Order Linear Equations | p. 119 |
Second Order Equations with Maple | p. 121 |
Comparison Methods | p. 124 |
The Interlacing of Zeros | p. 126 |
Proof of the Sturm Comparison Theorem | p. 127 |
A Geometric Method | p. 127 |
The Constant Coefficient Case | p. 128 |
The Variable Coefficient Case | p. 130 |
Airy's Equation | p. 130 |
Bessel's Equation | p. 131 |
Other Equations | p. 132 |
Second Order Equations | p. 135 |
Series Solutions | p. 149 |
Series Solutions | p. 150 |
Singular Points | p. 152 |
Laplace Transforms | p. 155 |
Differential Equations and Laplace Transforms | p. 157 |
Discontinuous Functions | p. 160 |
Differential Equations with Discontinuous Forcing | p. 162 |
Series Solutions and Laplace Transforms | p. 165 |
Higher Order Equations and Systems of First Order Equations | p. 177 |
Higher Order Linear Equations | p. 178 |
Systems of First Order Equations | p. 179 |
Linear First Order Systems | p. 179 |
Using Maple to Find Eigenpairs | p. 182 |
Phase Portraits | p. 186 |
Plotting a Single Trajectory | p. 187 |
Plotting Several Trajectories | p. 187 |
Numerical Solutions of First Order Systems | p. 189 |
Qualitative Theory for Systems of Differential Equations | p. 193 |
Systems of Differential Equations | p. 201 |
Glossary | p. 215 |
Sample Solutions | p. 223 |
Index | p. 243 |
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