9780534373887

A First Course in Differential Equations The Classic Fifth Edition

by
  • ISBN13:

    9780534373887

  • ISBN10:

    0534373887

  • Edition: 5th
  • Format: Hardcover
  • Copyright: 12/8/2000
  • Publisher: Cengage Learning
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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

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