Differential Equations with Matlab, 2nd Edition,9780471718123

Differential Equations with Matlab, 2nd Edition

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Edition: 2nd
ISBN13: 9780471718123
ISBN10: 0471718122
Format: Paperback
Pub. Date: 2005-01-01
Publisher(s): WILEY
List Price: $83.80

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Summary

"Differential Equations with MATLAB" (2nd ed.) by B. Hunt, R. Lipsman, J.Osborn and J.Rosenberg is a supplemental text that can enrich and enhance any first course in ordinary differential equations. Designed to accompany Wiley's ODE texts written by Boyce/DiPrima, Borrelli/Coleman and Lomen/Lovelock, this supplement helps instructors move towards an earlier use of numerical and geometric methods, place a greater emphasis on systems (including nonlinear ones), and increase discussions of both the benefits and possible pitfalls in numerical solution of ODEs. By providing an introduction to the software that is integrated with the relevant mathematics, "Differential Equations with MATLAB" can perfectly complement and enhance these texts.

Table of Contents

Preface v
Introduction
1(6)
Guiding Philosophy
1(2)
Student's Guide
3(1)
Instructor's Guide
4(2)
Matlab and Simulink
5(1)
ODE Chapters
5(1)
Computer Problem Sets
5(1)
A Word About Software Versions
6(1)
Getting Started with Matlab
7(6)
Platforms and Versions
7(1)
Installation
8(1)
Starting Matlab
8(1)
Typing in the Command Window
9(1)
Online Help
9(2)
Matlab Windows
11(1)
Ending a Session
12(1)
Doing Mathematics with Matlab
13(18)
Arithmetic
13(1)
Recovering from Problems
14(1)
Errors in Input
14(1)
Aborting Calculations
14(1)
Symbolic Computation
15(2)
Substituting in Symbolic Expressions
15(1)
Symbolic Expressions and Variable Precision Arithmetic
16(1)
Vectors
17(1)
Suppressing Output
18(1)
Functions
18(2)
Built-in Functions
18(1)
User-defined Functions
19(1)
Managing Variables
20(1)
Solving Equations
21(2)
Graphics
23(6)
Graphing with ezplot
23(1)
Modifying Graphs
24(1)
Graphing with plot
25(1)
Plotting Multiple Curves
26(1)
Parametric Plots
26(2)
Contour Plots
28(1)
Calculus
29(1)
Some Tips and Reminders
30(1)
Using M-files and M-books
31(16)
The Matlab Desktop
31(3)
The Workspace
31(1)
The Current Directory and Matlab Path
32(1)
The Command History
33(1)
M-files
34(4)
Script M-files
34(2)
Function M-files
36(1)
Cells
37(1)
Loops
38(1)
Presenting Your Results
38(7)
Presenting Graphics
39(1)
Pretty Printing
40(1)
``Publishing'' an M-file
41(1)
M-books
41(1)
Preparing Homework Solutions
42(3)
Debugging Your M-files
45(2)
Problem Set A: Practice with Matlab
47(28)
Solutions of Differential Equations
51(14)
Finding Symbolic Solutions
51(3)
Existence and Uniqueness
54(1)
Stability of Differential Equations
55(4)
Different Types of Symbolic Solutions
59(6)
A Qualitative Approach to Differential Equations
65(10)
Direction Field for a First Order Linear Equation
65(3)
Direction Field for a Non-Linear Equation
68(1)
Autonomous Equations
69(6)
Examples of Autonomous Equations
71(4)
Problem Set B: First Order Equations
75(56)
Numerical Methods
87(16)
Numerical Solutions Using Matlab
88(3)
Some Numerical Methods
91(7)
The Euler Method
92(3)
The Improved Euler Method
95(1)
The Runge-Kutta Method
96(1)
Inside ode45
97(1)
Round-off Error
98(1)
Controlling the Error in ode45
98(1)
Reliability of Numerical Methods
99(4)
Features of Matlab
103(18)
Data Classes
103(3)
String Manipulation
104(1)
Symbolic and Floating Point Numbers
105(1)
Structures
105(1)
Functions and Expressions
106(1)
More about M-files
107(2)
Variables in Script M-files
108(1)
Variables in Function M-files
108(1)
Structure of Function M-files
109(1)
Matrices
109(2)
Solving Linear Systems
110(1)
Calculating Eigenvalues and Eigenvectors
111(1)
Graphics
111(3)
Figure Windows
111(2)
Editing Figures
113(1)
Features of Matlab's Numerical ODE Solvers
114(5)
Evaluation of Numerical Solutions with deval
115(1)
Plotting Families of Numerical Solutions of ODEs
116(1)
Event Detection
117(2)
Troubleshooting
119(2)
The Most Common Mistakes
119(1)
Error and Warning Messages
120(1)
Using Simulink
121(10)
Constructing and Running a Simulink Model
121(6)
Output to the Workspace and How Simulink Works
127(4)
Problem Set C: Numerical Solutions
131(26)
Solving and Analyzing Second Order Linear Equations
139(18)
Second Order Equations with Matlab
141(4)
Second Order Equations with Simulink
145(2)
Comparison Methods
147(3)
The Interlacing of Zeros
148(1)
Proof of the Sturm Comparison Theorem
149(1)
A Geometric Method
150(7)
The Constant Coefficient Case
151(1)
The Variable Coefficient Case
152(1)
Airy's Equation
153(1)
Bessel's Equation
154(1)
Other Equations
155(2)
Problem Set D: Second Order Equations
157(36)
Series Solutions
171(12)
Series Solutions
172(2)
Singular Points
174(3)
Function M-files for Series Solutions
177(3)
Series Solutions Using maple
180(3)
Laplace Transforms
183(10)
Differential Equations and Laplace Transforms
185(3)
Discontinuous Functions
188(2)
Differential Equations with Discontinuous Forcing
190(3)
Problem Set E: Series Solutions and Laplace Transforms
193(38)
Higher Order Equations and Systems of First Order Equations
207(16)
Higher Order Linear Equations
208(1)
Systems of First Order Equations
209(7)
Linear First Order Systems
209(3)
Using Matlab to Find Eigenpairs
212(4)
Phase Portraits
216(7)
Plotting a Single Trajectory
216(1)
Plotting Several Trajectories
217(2)
Numerical Solutions of First Order Systems
219(4)
Qualitative Theory for Systems of Differential Equations
223(8)
Problem Set F: Systems of Differential Equations
231(16)
Glossary 247(12)
Sample Solutions 259(26)
Index 285

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