Elementary Differential Equations

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  • Edition: 6th
  • Format: Hardcover
  • Copyright: 2007-11-28
  • Publisher: Pearson
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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

Prefacep. vii
First-Order Differential Equationsp. 1
Differential Equations and Mathematical Modelsp. 1
Integrals as General and Particular Solutionsp. 10
Slope Fields and Solution Curvesp. 19
Separable Equations and Applicationsp. 32
Linear First-Order Equationsp. 46
Substitution Methods and Exact Equationsp. 59
Population Modelsp. 74
Acceleration-Velocity Modelsp. 85
Linear Equations of Higher Orderp. 100
Introduction: Second-Order Linear Equationsp. 100
General Solutions of Linear Equationsp. 113
Homogeneous Equations with Constant Coefficientsp. 124
Mechanical Vibrationsp. 135
Nonhomogeneous Equations and Undetermined Coefficientsp. 148
Forced Oscillations and Resonancep. 162
Electrical Circuitsp. 173
Endpoint Problems and Eigenvaluesp. 180
Power Series Methodsp. 194
Introduction and Review of Power Seriesp. 194
Series Solutions Near Ordinary Pointsp. 207
Regular Singular Pointsp. 218
Method of Frobenius: The Exceptional Casesp. 233
Bessel's Equationp. 248
Applications of Bessel Functionsp. 257
Laplace Transform Methodsp. 266
Laplace Transforms and Inverse Transformsp. 266
Transformation of Initial Value Problemsp. 277
Translation and Partial Fractionsp. 289
Derivatives, Integrals, and Products of Transformsp. 297
Periodic and Piecewise Continuous Input Functionsp. 304
Impulses and Delta Functionsp. 316
Linear Systems of Differential Equationsp. 326
First-Order Systems and Applicationsp. 326
The Method of Eliminationp. 338
Matrices and Linear Systemsp. 347
The Eigenvalue Method for Homogeneous Systemsp. 366
Second-Order Systems and Mechanical Applicationsp. 381
Multiple Eigenvalue Solutionsp. 393
Matrix Exponentials and Linear Systemsp. 407
Nonhomogeneous Linear Systemsp. 420
Numerical Methodsp. 430
Numerical Approximation: Euler's Methodp. 430
A Closer Look at the Euler Methodp. 442
The Runge-Kutta Methodp. 453
Numerical Methods for Systemsp. 464
Nonlinear Systems and Phenomenap. 480
Equilibrium Solutions and Sta
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