Elementary Differential Equations

by Edwards, C. Henry; Penney, David E.

• ISBN13: 9780132397308
• ISBN10: 0132397307
• Edition: 6th
• Format: Hardcover
• Copyright: 2007-11-28
• Publisher: Pearson

Summary

The Sixth Edition of this acclaimed differential equations book remains the same classic volume it's always been, but has been polished and sharpened to serve readers even more effectively. Offers precise and clear-cut statements of fundamental existence and uniqueness theorems to allow understanding of their role in this subject. Features a strong numerical approach that emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques. Inserts new graphics and text where needed for improved accessibility. A useful reference for readers who need to brush up on differential equations.

Author Biography

C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979). During the 1990s he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students.

David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L. Bruce Treybig) while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran's Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee's research team's primary focus was on the active transport of sodium ions by biological membranes. Penney's primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure. He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms. Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium. During his tenure at the University of Georgia he received numerous University-wide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects. He is the author of research papers in number theory and topology and is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.

Table of Contents

Preface	p. vii
First-Order Differential Equations	p. 1
Differential Equations and Mathematical Models	p. 1
Integrals as General and Particular Solutions	p. 10
Slope Fields and Solution Curves	p. 19
Separable Equations and Applications	p. 32
Linear First-Order Equations	p. 46
Substitution Methods and Exact Equations	p. 59
Population Models	p. 74
Acceleration-Velocity Models	p. 85
Linear Equations of Higher Order	p. 100
Introduction: Second-Order Linear Equations	p. 100
General Solutions of Linear Equations	p. 113
Homogeneous Equations with Constant Coefficients	p. 124
Mechanical Vibrations	p. 135
Nonhomogeneous Equations and Undetermined Coefficients	p. 148
Forced Oscillations and Resonance	p. 162
Electrical Circuits	p. 173
Endpoint Problems and Eigenvalues	p. 180
Power Series Methods	p. 194
Introduction and Review of Power Series	p. 194
Series Solutions Near Ordinary Points	p. 207
Regular Singular Points	p. 218
Method of Frobenius: The Exceptional Cases	p. 233
Bessel's Equation	p. 248
Applications of Bessel Functions	p. 257
Laplace Transform Methods	p. 266
Laplace Transforms and Inverse Transforms	p. 266
Transformation of Initial Value Problems	p. 277
Translation and Partial Fractions	p. 289
Derivatives, Integrals, and Products of Transforms	p. 297
Periodic and Piecewise Continuous Input Functions	p. 304
Impulses and Delta Functions	p. 316
Linear Systems of Differential Equations	p. 326
First-Order Systems and Applications	p. 326
The Method of Elimination	p. 338
Matrices and Linear Systems	p. 347
The Eigenvalue Method for Homogeneous Systems	p. 366
Second-Order Systems and Mechanical Applications	p. 381
Multiple Eigenvalue Solutions	p. 393
Matrix Exponentials and Linear Systems	p. 407
Nonhomogeneous Linear Systems	p. 420
Numerical Methods	p. 430
Numerical Approximation: Euler's Method	p. 430
A Closer Look at the Euler Method	p. 442
The Runge-Kutta Method	p. 453
Numerical Methods for Systems	p. 464
Nonlinear Systems and Phenomena	p. 480
Equilibrium Solutions and Sta
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