A First Course in Differential Equations The Classic Fifth Edition

by Zill, Dennis G.

• ISBN13: 9780534373887
• ISBN10: 0534373887
• Additional ISBN(s): 9780357760192, 9780534418977
• Edition: 5th
• Format: Hardcover
• Copyright: 2000-12-08
• Publisher: Cengage Learning
• More Book Details

Summary

The CLASSIC EDITION of Zill's respected book was designed for instructors who prefer not to emphasize technology, modeling, and applications, but instead want to focus on fundamental theory and techniques. Zill's CLASSIC EDITION, a reissue of the fifth edition, offers his excellent writing style, a flexible organization, an accessible level of presentation, and a wide variety of examples and exercises, all of which make it easy to teach from and easy for readers to understand and use.

Table of Contents

A Word from the Publisher	ix
Preface to the Fifth Edition	xi
Introduction to Differential Equations	1	(27)
Basic Definitions and Terminology	2	(9)
Some Mathematical Models	11	(17)
Review	25	(1)
Review Exercises	26	(2)
First-Order Differential Equations	28	(47)
Preliminary Theory	29	(4)
Separable Variables	33	(7)
Homogeneous Equations	40	(6)
Exact Equations	46	(8)
Linear Equations	54	(8)
Equations of Bernoulli, Ricatti, and Clairaut	62	(5)
Substitutions	67	(3)
Picard's Method	70	(5)
Review	72	(1)
Review Exercises	73	(2)
Applications of First-Order Differential Equations	75	(36)
Orthogonal Trajectories	76	(5)
Applications of Linear Equations	81	(12)
Applications of Nonlinear Equations	93	(18)
Review	103	(1)
Review Exercises	104	(2)
Essay: Population Dynamics	106	(5)
Michael Olinick
Linear Differential Equations of Higher-Order	111	(72)
Preliminary Theory	112	(21)
Initial-Value and Boundary-Value Problems	112	(3)
Linear Dependence and Linear Independence	115	(5)
Solutions of Linear Equations	120	(13)
Constructing a Second Solution from a Known Solution	133	(5)
Homogeneous Linear Equations with Constant Coefficients	138	(8)
Undetermined Coefficients-Superposition Approach	146	(11)
Differential Operators	157	(5)
Undetermined Coefficient---Annihilator Approach	162	(7)
Variation of Parameters	169	(14)
Review	175	(2)
Review Exercises	177	(2)
Essay: Chaos	179	(4)
John H. Hubbard
Applications of Second-Order Differential Equations: Vibrational Models	183	(38)
Simple Harmonic Motion	184	(8)
Damped Motion	192	(8)
Forced Motion	200	(9)
Electric Circuits and Other Analogous Systems	209	(12)
Review	214	(1)
Review Exercises	215	(3)
Essay: Tacoma Narrows Suspension Bridge Collapse	218	(3)
Gilbert N. Lewis
Differential Equations with Variable Coefficients	221	(59)
Cauchy-Euler Equation	222	(8)
Review of Power Series; Power Series Solutions	230	(9)
Solutions About Ordinary Points	239	(9)
Solutions About Singular Points	248	(17)
Regular Singular Points; Method of Frobenius---Case I	248	(9)
Method of Frobenius---Cases II and III	257	(8)
Two Special Equations	265	(15)
Solution of Bessel's Equation	266	(5)
Solution of Legendre's Equation	271	(6)
Review	277	(1)
Review Exercises	278	(2)
Laplace Transform	280	(55)
Laplace Transform	281	(9)
Inverse Transform	290	(6)
Translation Theorems and Derivatives of a Transform	296	(11)
Transforms of Derivatives, Integrals, and Periodic Functions	307	(7)
Applications	314	(14)
Dirac Delta Function	328	(7)
Review	332	(1)
Review Exercises	332	(3)
Systems of Linear Differential Equations	335	(86)
Operator Method	336	(7)
Laplace Transform Method	343	(7)
Systems of Linear First-Order Equations	350	(5)
Introduction to Matrices	355	(20)
Basic Definitions and Theory	355	(9)
Gaussian and Gauss-Jordan Elimination Methods	364	(4)
The Eigenvalue Problem	368	(7)
Matrices and Systems of Linear First-Order Equations	375	(16)
Preliminary Theory	375	(9)
A Fundamental Matrix	384	(7)
Homogeneous Linear Systems	391	(14)
Distinct Real Eigenvalues	391	(3)
Complex Eigenvalues	394	(4)
Repeated Eigenvalues	398	(7)
Undetermined Coefficients	405	(4)
Variation of Parameters	409	(4)
Matrix Exponential	413	(8)
Review	416	(2)
Review Exercises	418	(3)
Numerical Methods for Ordinary Differential Equations	421	(1)
Direction Fields	422	(4)
The Euler Methods	426	(6)
The Three-Term Taylor Method	432	(3)
The Runge-Kutta Method	435	(4)
Multistep Methods	439	(3)
Errors and Stability	442	(6)
Higher-Order Equations and Systems	448	(4)
Second-Order Boundary-Value Problems	452	(4)
Review	456	(1)
Review Exercises	457	(2)
Essay: Nerve Impulse Models	459
C. J. Knickerbocker
APPENDIXES
I Gamma Function	1	(3)
II Laplace Transforms	4	(3)
III Review of Determinants	7	(4)
IV Complex Numbers	11
Answers to Odd-Numbered Problems	1	(1)
Index	1