Elementary Differential Equations and Boundary Value Problems, 7th Edition

by William E. Boyce (Edward P. Hamilton Professor Emeritus); Richard C. DiPrima (Rensselaer Polytechnic Institute)

• ISBN13: 9780471319993
• ISBN10: 0471319996
• Edition: 7th
• Format: Hardcover
• Copyright: 2000-08-01
• Publisher: Wiley

Summary

Written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year. The main prerequisite is a working knowledge of calculus. The environment in which instructors teach, and students learn differential equations has changed enormously in the past few years and continues to evolve at a rapid pace. Computing equipment of some kind, whether a graphing calculator, a notebook computer, or a desktop workstation is available to most students. The seventh edition of this classic text reflects this changing environment, while at the same time, it maintains its great strengths - a contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. In addition many new problems have been added and a reorganisation of the material makes the concepts even clearer and more comprehensible. Like its predecessors, this edition 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 currently the Edward P. Hamilton Distinguished Professor Emeritus of Science Education (Department of Mathematical Sciences) at Rensselaer Richard C. DiPrima (deceased) received his B.S., M.S., and Ph.D. degrees in Mathematics from Carnegie-Mellon University. He joined the faculty of Rensselaer Polytechnic Institute after holding research positions at MIT, Harvard, and Hughes Aircraft. He held the Eliza Ricketts Foundation Professorship of Mathematics at Rensselaer

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)
Partial Differential Equations and Fourier Series	541	(80)
Two-Point Boundary Valve Problems	541	(6)
Fourier Series	547	(11)
The Fourier Convergence Theorem	558	(6)
Even and Odd Functions	564	(9)
Separation of Variables; Heat Conduction in a Rod	573	(8)
Other Heat Conduction Problems	581	(10)
The Wave Equation; Vibrations of an Elastic String	591	(13)
Laplace's Equation	604	(17)
Derivation of the Heat Conduction Equation	614	(3)
Derivation of the Wave Equation	617	(4)
Boundary Value Problems and Sturm-Liouville Theory	621	(58)
The Occurrence of Two Point Boundary Value Problems	621	(8)
Strum--Liouville Boundary Value Problems	629	(12)
Nonhomogeneous Boundary Value Problems	641	(15)
Singular Sturm--Liouville Problems	656	(7)
Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion	663	(6)
Series of Orthogonal Functions: Mean Convergence	669	(10)
Answers to Problems	679	(58)
Index	737