Differential Equations With Boundary-Value Problems

by Zill, Dennis G.; Cullen, Michael R.

• ISBN13: 9780534380021
• ISBN10: 0534380026
• Edition: 5th
• Format: Hardcover
• Copyright: 2000-10-05
• Publisher: Brooks Cole

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