Differential Equations with Maple

ISBN-10: 0471773174
ISBN-13: 9780471773177
Edition: 3rd 2009
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Description: This supplement introduces version 4 of the popular mathematical software system Maple as a tool for analysing differential equations. It emphasises an integrated approach using symbolic, numerical, graphical and qualitative techniques.

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Book details

List price: $62.95
Edition: 3rd
Copyright year: 2009
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/29/2008
Binding: Paperback
Pages: 264
Size: 7.50" wide x 9.25" long x 0.75" tall
Weight: 1.298
Language: English

This supplement introduces version 4 of the popular mathematical software system Maple as a tool for analysing differential equations. It emphasises an integrated approach using symbolic, numerical, graphical and qualitative techniques.

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

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