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Elementary Differential Equations, 7th Edition,9780471319986
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Elementary Differential Equations, 7th Edition

by ;
Edition:
7th
ISBN13:

9780471319986

ISBN10:
0471319988
Format:
Hardcover
Pub. Date:
7/1/2000
Publisher(s):
Wiley
List Price: $128.00
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Summary

This revision of Boyce & DiPrima's market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Concepts are clearer and more comprehensible with a bit of new reorganization. An abundance of new problems have been added to the problem sets, with special attention paid to incorporating computer technology. Like previous editions, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences.

Author Biography

William E. Boyce is the Edward P. Hamilton Distinguished Professor Emeritus of Science Education (Department of Mathematical Sciences) at Rensselaer Richard C. DiPrima is on the faculty of Rensselaer Polytechnic Institute

Table of Contents

Preface vii
Introduction
1(28)
Some Basic Mathematical Models; Direction Fields
1(8)
Solutions of Some Differential Equations
9(8)
Classification of Differential Equations
17(6)
Historical Remarks
23(6)
First Order Differential Equations
29(100)
Linear Equations with Variable Coefficients
29(11)
Separable Equations
40(7)
Modeling with First Order Equations
47(17)
Differences Between Linear and Nonlinear Equations
64(10)
Autonomous Equations and Population Dynamics
74(15)
Exact Equations and Integrating Factors
89(7)
Numerical Approximations: Euler's Method
96(9)
The Existence and Uniqueness Theorem
105(10)
First Order Difference Equations
115(14)
Second Order Linear Equations
129(80)
Homogeneous Equations with Constant Coefficients
129(8)
Fundamental Solutions of Linear Homogeneous Equations
137(10)
Linear Independence and the Wronskian
147(6)
Complex Roots of the Characteristic Equation
153(7)
Repeated Roots; Reduction of Order
160(9)
Nonhomogeneous Equations; Method of Undetermined Coefficients
169(10)
Variation of Parameters
179(7)
Mechanical and Electrical Vibrations
186(14)
Forced Vibrations
200(9)
Higher Order Linear Equations
209(22)
General Theory of nth Order Linear Equations
209(5)
Homogeneous Equations with Constant Coeffients
214(8)
The Method of Undetermined Coefficients
222(4)
The Method of Variation of Parameters
226(5)
Series Solutions of Second Order Linear Equations
231(62)
Review of Power Series
231(7)
Series Solutions near an Ordinary Point, Part I
238(11)
Series Solutions near an Ordinary Point, Part II
249(6)
Regular Singular Points
255(5)
Euler Equations
260(7)
Series Solutions near a Regular Singular Point, Part I
267(5)
Series Solutions near a Regular Singular Point, Part II
272(8)
Bessel's Equation
280(13)
The Laplace Transform
293(46)
Definition of the Laplace Transform
293(6)
Solution of Initial Value Problems
299(11)
Step Functions
310(7)
Differential Equations with Discontinuous Forcing Functions
317(7)
Impulse Functions
324(6)
The Convolution Integral
330(9)
Systems of First Order Linear Equations
339(80)
Introduction
339(9)
Review of Matrices
348(9)
Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
357(11)
Basic Theory of Systems of First Order Linear Equations
368(5)
Homogeneous Linear Systems with Constant Coefficients
373(11)
Complex Eigenvalues
384(9)
Fundamental Matrices
393(8)
Repeated Eigenvalues
401(10)
Nonhomogeneous Linear Systems
411(8)
Numerical Methods
419(40)
The Euler or Tangent Line Method
419(11)
Improvements on the Euler Method
430(5)
The Runge-Kutta Method
435(4)
Multistep Methods
439(6)
More on Errors; Stability
445(10)
Systems of First Order Equations
455(4)
Nonlinear Differential Equations and Stability
459(82)
The Phase Plane; Linear Systems
459(12)
Autonomous Systems and Stability
471(8)
Almost Linear Systems
479(12)
Competing Species
491(12)
Predator-Prey Equations
503(8)
Liapunov's Second Method
511(10)
Periodic Solutions and Limit Cycles
521(11)
Chaos and Strange Attractors; the Lorenz Equations
532(9)
Answer to Problems 541(46)
Index 587


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