9780471773177

includes concise instructions for using Maple on any standard computer platform: Windows, Macintosh, or UNIX, including Linux can easily be used in conjunction with most Ordinary Differential Equations textbooks

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
Table of Contents provided by Ingram. All Rights Reserved.

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Differential Equations with Maple, 3rd Edition

0471773174

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