Differential Equations With Boundary-Value Problems,9780534380021

Differential Equations With Boundary-Value Problems

by ;
Edition: 5th
ISBN13: 9780534380021
ISBN10: 0534380026
Format: Hardcover
Pub. Date: 2000-10-05
Publisher(s): Brooks Cole
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Summary

Master differential equations and succeed in your course DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS with accompanying CD-ROM and technology! Straightfoward and readable, this mathematics text provides you with tools such as examples, explanations, definitions, and applications designed to help you succeed. The accompanying DE Tools CD-ROM makes helps you master difficult concepts through twenty-one demonstration tools such as Project Tools and Text Tools. Studying is made easy with iLrn Tutorial, a text-specific, interactive tutorial software program that gives the practice you need to succeed.

Table of Contents

Preface xi
Acknowledgments xv
Introduction to Differential Equations
1(38)
Definitions and Terminology
2(13)
Initial-Value Problems
15(7)
Differential Equations as Mathematical Models
22(17)
Chapter 1 in Review
37(2)
First-Order Differential Equations
39(56)
Solution Curves Without the Solution
40(11)
Separable Variables
51(9)
Linear Equations
60(12)
Exact Equations
72(8)
Solutions by Substitutions
80(6)
A Numerical Solution
86(9)
Chapter 2 in Review
92(3)
Modeling with First-Order Differential Equations
95(43)
Linear Equations
96(13)
Nonlinear Equations
109(12)
Systems of Linear and Nonlinear Differential Equations
121(17)
Chapter 3 in Review
130(3)
Project Module: Harvesting of Renewable Natural Resources
133(5)
Gilbert N. Lewis
Higher-Order Differential Equations
138(77)
Preliminary Theory: Linear Equations
139(15)
Initial-Value and Boundary-Value Problems
139(3)
Homogeneous Equations
142(6)
Nonhomogeneous Equations
148(6)
Reduction of Order
154(4)
Homogeneous Linear Equations with Constant Coefficients
158(9)
Undetermined Coefficients--Superposition Approach
167(11)
Undetermined Coefficients--Annihilator Approach
178(10)
Variation of Parameters
188(5)
Cauchy-Euler Equation
193(8)
Solving Systems of Linear Equations by Elimination
201(6)
Nonlinear Equations
207(8)
Chapter 4 in Review
212(3)
Modeling with Higher-Order Differential Equations
215(52)
Linear Equations: Initial-Value Problems
216(21)
Spring/Mass Systems: Free Undamped Motion
216(4)
Spring/Mass Systems: Free Damped Motion
220(4)
Spring/Mass Systems: Driven Motion
224(3)
Series Circuit Analogue
227(10)
Linear Equations: Boundary-Value Problems
237(10)
Nonlinear Equations
247(20)
Chapter 5 in Review
259(4)
Project Module: The Collapse of the Tacoma Narrows Suspension Bridge
263(4)
Gilbert N. Lewis
Series Solutions of Linear Equations
267(39)
Solutions About Ordinary Points
268(12)
Review of Power Series
268(3)
Power Series Solutions
271(9)
Solutions About Singular Points
280(12)
Two Special Equations
292(14)
Chapter 6 in Review
304(2)
The Laplace Transform
306(58)
Definition of the Laplace Transform
307(7)
Inverse Transform and Transforms of Derivatives
314(10)
Translation Theorems
324(14)
Translation on the s-Axis
324(4)
Translation on the t-Axis
328(10)
Additional Operational Properties
338(13)
Dirac Delta Function
351(3)
Systems of Linear Equations
354(10)
Chapter 7 in Review
361(3)
Systems of Linear First-Order Differential Equations
364(46)
Preliminary Theory
365(10)
Homogeneous Linear Systems with Constant Coefficients
375(18)
Distinct Real Eigenvalues
376(4)
Repeated Eigenvalues
380(4)
Complex Eigenvalues
384(9)
Variation of Parameters
393(6)
Matrix Exponential
399(11)
Chapter 8 in Review
404(2)
Project Module: Earthquake Shaking of Multistory Buildings
406(4)
Gilbert N. Lewis
Numerical Solutions of Ordinary Differential Equations
410(29)
Euler Methods and Error Analysis
411(6)
Runge-Kutta Methods
417(7)
Multistep Methods
424(3)
Higher-Order Equations and Systems
427(6)
Second-Order Boundary-Value Problems
433(6)
Chapter 9 in Review
438(1)
Plane Autonomous Systems and Stability
439(44)
Autonomous Systems, Critical Points, and Periodic Solutions
440(8)
Stability of Linear Systems
448(10)
Linearization and Local Stability
458(12)
Modeling Using Autonomous Systems
470(13)
Chapter 10 in Review
480(3)
Orthogonal Functions and Fourier Series
483(38)
Orthogonal Functions
484(5)
Fourier Series
489(6)
Fourier Cosine and Sine Series
495(9)
Sturm-Liouville Problem
504(7)
Bessel and Legendre Series
511(10)
Fourier-Bessel Series
512(3)
Fourier-Legendre Series
515(4)
Chapter 11 in Review
519(2)
Partial Differential Equations and Boundary-Value Problems in Rectangular Coordinates
521(40)
Separable Partial Differential Equations
522(5)
Classical Equations and Boundary-Value Problems
527(6)
Heat Equation
533(3)
Wave Equation
536(6)
Laplace's Equation
542(5)
Nonhomogeneous Equations and Boundary Conditions
547(4)
Orthogonal Series Expansions
551(4)
Boundary-Value Problems Involving Fourier Series in Two Variables
555(6)
Chapter 12 in Review
559(2)
Boundary-Value Problems In Other Coordinate Systems
561(20)
Problems Involving Laplace's Equation in Polar Coordinates
562(5)
Problems in Polar and Cylindrical Coordinates: Bessel Functions
567(8)
Problems in Spherical Coordinates: Legendre Polynomials
575(6)
Chapter 13 in Review
578(3)
Integral Transform Method
581(29)
Error Function
582(2)
Applications of the Laplace Transform
584(11)
Fourier Integral
595(6)
Fourier Transforms
601(9)
Chapter 14 in Review
607(3)
Numerical Solutions of Partial Differential Equations
610
Elliptic Equations
611(6)
Parabolic Equations
617(8)
Hyperbolic Equations
625
Chapter 15 in Review
630
APPENDIXES 1(1)
I Gamma Function
1(2)
II Introduction to Matrices
3(22)
III Laplace Transforms
25
Selected Answers for Odd-Numbered Problems 1(1)
Index 1

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