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Differential Equations with Boundary Value Problems,9780130911063
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Differential Equations with Boundary Value Problems

by ; ;
Edition:
1st
ISBN13:

9780130911063

ISBN10:
0130911062
Format:
Hardcover
Pub. Date:
1/1/2002
Publisher(s):
Prentice Hall
List Price: $112.00

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Summary

Ideal for one or two term first courses in differential equations for engineering, math, biology, and finance majors. This text strikes a balance between the traditional and the modern. It combines the traditional material with a modern systems emphasis. It offers flexibility of use that will allow faculty at a variety of institutions to use the book with extensive problem sets.

Table of Contents

Preface ix
Introduction to Differential Equations
1(17)
Differential Equation Models
2(5)
The Derivative
7(3)
Integration
10(8)
First-Order Equations
18(105)
Differential Equations and Solutions
18(13)
Solutions to Separable Equations
31(13)
Models of Motion
44(10)
Linear Equations
54(10)
Mixing Problems
64(9)
Exact Differential Equations
73(17)
Existence and Uniqueness of Solutions
90(12)
Dependence of Solutions on Initial Conditions
102(5)
Autonomous Equations and Stability
107(16)
Project 2.10 The Daredevil Skydiver
120(3)
Modeling and Applications
123(40)
Modeling Population Growth
124(14)
Models and the Real World
138(5)
Personal Finance
143(9)
Electrical Circuits
152(11)
Project 3.5 The Spruce Budworm
158(3)
Project 3.6 Social Security, Now or Later
161(2)
Second-Order Equations
163(68)
Definitions and Examples
163(11)
Second-Order Equations and Systems
174(5)
Linear, Homogeneous Equations with Constant Coefficients
179(11)
Harmonic Motion
190(9)
Inhomogeneous Equations; the Method of Undetermined Coefficients
199(10)
Variation of Parameters
209(6)
Forced Harmonic Motion
215(16)
Project 4.8 Nonlinear Oscillators
228(3)
The Laplace Transform
231(70)
The Definition of the Laplace Transform
232(9)
Basic Properties of the Laplace Transform
241(7)
The Inverse Laplace Transform
248(8)
Using the Laplace Transform to Solve Differential Equations
256(10)
Discontinuous Forcing Terms
266(14)
The Delta Function
280(7)
Convolutions
287(11)
Summary
298(3)
Project 5.9 Forced Harmonic Oscillators
299(2)
Numerical Methods
301(34)
Euler's Method
302(12)
Runge-Kutta Methods
314(8)
Numerical Error Comparisons
322(5)
Practical Use of Solvers
327(5)
A Cautionary Tale
332(3)
Project 6.6 Numerical Error Comparison
334(1)
Matrix Algebra
335(61)
Vectors and Matrices
335(13)
The Geometry of Systems of Linear Equations
348(5)
Solving Systems of Equations
353(9)
Properties of Solution Sets
362(9)
Subspaces
371(13)
Determinants
384(12)
An Introduction to Systems
396(48)
Definitions and Examples
396(9)
Geometric Interpretation of Solutions
405(12)
Qualitative Analysis
417(8)
Linear Systems
425(19)
Project 8.5 Long-Term Behavior of Solutions
441(3)
Linear Systems with Constant Coefficents
444(101)
Overview of the Technique
444(8)
Planar Systems
452(14)
Phase Plane Portraits
466(18)
Higher Dimensional Systems
484(8)
The Exponential of a Matrix
492(18)
Qualitative Analysis of Lienar Systems
510(5)
Higher-Order Linear Equations
515(13)
Inhomogeneous Linear Systems
528(17)
Project 9.9 Phase Plane Portraits
538(1)
Project 9.10 Oscillations of Linear Molecules
539(6)
Nonlinear Systems
545(92)
The Linearization of a Nonlinear System
545(14)
Long-Term Behavior of Solutions
559(7)
Invariant Sets and the Use of Nullclines
566(8)
Long-Term Behavior of Solutions to Planar Systems
574(12)
Conserved Quantities
586(6)
Nonlinear Mechanics
592(17)
The Method of Lyapunov
609(10)
Predator-Prey Systems
619(18)
Project 10.9 Human Immune Response to Infectious Disease
631(3)
Project 10.10 Analysis of Competing Species
634(3)
Series Solutions to Differential Equations
637(75)
Review of Power Series
638(12)
Series Solutions Near Ordinary Points
650(12)
Legendre's Equation
662(6)
Types of Singular Points---Euler's Equation
668(9)
Series Solutions Near Regular Singular Points
677(13)
Solutions in the Exceptional Cases
690(11)
Bessel's Equation and Bessel Functions
701(11)
Fourier Series
712(38)
Computation of Fourier Series
713(11)
Convergence of Fourier Series
724(9)
Fourier Cosine and Sine Series
733(5)
The Complex Form of a Fourier Series
738(3)
The Discrete Fourier Transform and the FFT
741(9)
Partial Differential Equations
750
Derivation of the Heat Equation
750
Separation of Variables for the Heat Equation
756
The Wave Equation
768
Laplace's Equation
778
Laplace's Equation on a Disk
785
Sturm Liouville Problems
791
Orthogonality and Generalized Fourier Series
801
Temperature in a Ball---Legendre Polynomials
810
Time Dependent PDEs in Higher Dimension
814
Domains with Circular Symmetry---Bessel Functions
821
Answers to Odd-Numbered Problems A-1
Index I-1


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