Differential Equations with Matlab, 2nd Edition

by Brian R. Hunt; Ronald L. Lipsman; John E. Osborn; Jonathan Rosenberg

• ISBN13: 9780471718123
• ISBN10: 0471718122
• Edition: 2nd
• Format: Paperback
• Copyright: 2005-01-01
• Publisher: WILEY

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