| |
| |
Preface | |
| |
| |
| |
Introduction | |
| |
| |
| |
Guiding Philosophy | |
| |
| |
| |
Student's Guide | |
| |
| |
| |
Instructor's Guide | |
| |
| |
| |
Maple | |
| |
| |
| |
ODE Chapters | |
| |
| |
| |
Computer Problem Sets | |
| |
| |
| |
A Word about Software Versions | |
| |
| |
| |
Getting Started with Maple | |
| |
| |
| |
Platforms and Versions | |
| |
| |
| |
Installation | |
| |
| |
| |
Starting Maple | |
| |
| |
| |
Maple Input | |
| |
| |
| |
Online Help | |
| |
| |
| |
Ending a Session | |
| |
| |
| |
Doing Mathematics with Maple | |
| |
| |
| |
Arithmetic | |
| |
| |
| |
Symbolic Computation | |
| |
| |
| |
Assignments | |
| |
| |
| |
Working with Output | |
| |
| |
| |
Recovering from Problems | |
| |
| |
| |
Errors in Input | |
| |
| |
| |
Aborting Calculations | |
| |
| |
| |
Suppressing Output | |
| |
| |
| |
The Restart Command | |
| |
| |
| |
Equations | |
| |
| |
| |
Solving Equations | |
| |
| |
| |
Functions and Expressions | |
| |
| |
| |
Built-in Functions | |
| |
| |
| |
User-defined Functions | |
| |
| |
| |
Expressions | |
| |
| |
| |
Substitution | |
| |
| |
| |
Sequences, Sets, and Lists | |
| |
| |
| |
Packages | |
| |
| |
| |
Graphics | |
| |
| |
| |
Plotting Functions and Expressions | |
| |
| |
| |
Plotting Multiple Curves | |
| |
| |
| |
Plotting Points | |
| |
| |
| |
Adding Text to a Plot | |
| |
| |
| |
Parametric Plots | |
| |
| |
| |
Implicit Plots | |
| |
| |
| |
Contour Plots | |
| |
| |
| |
Calculus | |
| |
| |
| |
More on Sequences, Lists, and Sets | |
| |
| |
| |
Procedures | |
| |
| |
| |
Some Tips and Reminders | |
| |
| |
| |
Using Maple Documents | |
| |
| |
| |
The Maple Window | |
| |
| |
| |
Organization of a Document | |
| |
| |
| |
Document Blocks | |
| |
| |
| |
Graphics | |
| |
| |
| |
Preparing Homework Solutions | |
| |
| |
| |
Practice with Maple | |
| |
| |
| |
Solutions of Differential Equations | |
| |
| |
| |
Finding Symbolic Solutions | |
| |
| |
| |
Existence and Uniqueness | |
| |
| |
| |
Stability of Differential Equations | |
| |
| |
| |
Different Types of Symbolic Solutions | |
| |
| |
| |
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 | |
| |
| |
| |
First Order Equations | |
| |
| |
| |
Numerical Methods | |
| |
| |
| |
Numerical Solutions Using Maple | |
| |
| |
| |
Some Numerical Methods | |
| |
| |
| |
The Euler Method | |
| |
| |
| |
The Improved Euler Method | |
| |
| |
| |
The Runge-Kutta Method | |
| |
| |
| |
Inside dsolve(..., numeric) | |
| |
| |
| |
Round-off Error | |
| |
| |
| |
Controlling the Error in dsolve(..., numeric) | |
| |
| |
| |
Reliability of Numerical Methods | |
| |
| |
| |
Features of Maple | |
| |
| |
| |
Names and Values | |
| |
| |
| |
Clearing Values | |
| |
| |
| |
Vectors and Matrices | |
| |
| |
| |
Solving Linear Systems | |
| |
| |
| |
Calculating Eigenvalues and Eigenvectors | |
| |
| |
| |
Plots for ODEs | |
| |
| |
| |
Commands for Plotting Direction Fields | |
| |
| |
| |
Plotting Families of Numerical Solutions of ODEs | |
| |
| |
| |
More about D Eplot | |
| |
| |
| |
Stopping Conditions | |
| |
| |
| |
Numerical Solutions of Higher Order Differential Equations | |
| |
| |
| |
Troubleshooting | |
| |
| |
| |
The Common Mistakes | |
| |
| |
| |
Error and Warning Messages | |
| |
| |
| |
Numerical Solutions | |
| |
| |
| |
Solving and Analyzing Second Order Linear Equations | |
| |
| |
| |
Second Order Equations with Maple | |
| |
| |
| |
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 | |
| |
| |
| |
Second Order Equations | |
| |
| |
| |
Series Solutions | |
| |
| |
| |
Series Solutions | |
| |
| |
| |
Singular Points | |
| |
| |
| |
Laplace Transforms | |
| |
| |
| |
Differential Equations and Laplace Transforms | |
| |
| |
| |
Discontinuous Functions | |
| |
| |
| |
Differential Equations with Discontinuous Forcing | |
| |
| |
| |
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 Maple to Find Eigenpairs | |
| |
| |
| |
Phase Portraits | |
| |
| |
| |
Plotting a Single Trajectory | |
| |
| |
| |
Plotting Several Trajectories | |
| |
| |
| |
Numerical Solutions of First Order Systems | |
| |
| |
| |
Qualitative Theory for Systems of Differential Equations | |
| |
| |
| |
Systems of Differential Equations | |
| |
| |
Glossary | |
| |
| |
Sample Solutions | |
| |
| |
Index | |