Differential Equations: Computing and Modeling / Edition 5

Differential Equations: Computing and Modeling / Edition 5

by C. Henry Edwards
ISBN-10:
0321816250
ISBN-13:
2900321816251
Pub. Date:
09/18/2014
Publisher:
Pearson
Differential Equations: Computing and Modeling / Edition 5

Differential Equations: Computing and Modeling / Edition 5

by C. Henry Edwards
$152.62
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Overview

A back–to–basics course is stressed. The computer permits the cutting of highly specialized ODEs to focus in greater depth, from a mathematical perspective, on the core ideas.

Offers an unusually early introduction to mathematical modeling, stability and qualitative properties of differential equations and to numerical methods (Ch. 2).

A qualitative approach is stressed throughout by emphasizing dynamical systems and phase portraits.

Provides an unusually flexible treatment of linear systems:

  • Ch. 4 offers an early, intuitive introduction to first-order systems, models, and numerical computer methods. Includes numerical algorithms presented in parallel fashion for systems ranging from the TI-85 graphics calculator to MATLAB.
  • Ch. 5 begins with a self-contained treatment of the necessary linear algebra, and then presents the eigenvalue approach to linear systems. Includes an large number of applications (ranging from railway cars to earthquakes) of all the various cases of the eigenvalue method.

Presents a broad discussion of nonlinear systems and phenomena -- ranging from phase plane analysis to ecological and mechanical systems to an innovative concluding section on chaos and bifurcation in dynamical systems.

  • presents an elementary introduction to such contemporary topics such as period-doubling in biological and mechanical systems, the pitchfork diagram, and the Lorenz strange attractor -- all illustrated with vivid computer graphics.

Shows how the ready availability of computational aids can clarify traditional manual topics (i.e. undetermined coefficients and Laplace transforms).

Brings numeric and symbolic solutions of differential equations to life -- features 180 computer-generated graphics that vividly illustrate slope fields, solution curves, and phase plane portraits.

Contains approximately 2,000 carefully graded problems -- ranging from routine computational exercises to conceptual and applied problems.

Contains three dozen Computer Projects that illustrate the use of computer algebra systems (e.g., Maple, Mathematica, and MATLAB) -- to actively engage students in the application of new technology.


Product Details

ISBN-13: 2900321816251
Publisher: Pearson
Publication date: 09/18/2014
Series: Edwards, Penney & Calvis, Differential Equations: Computing and Modeling Series
Edition description: New Edition
Pages: 576
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

About the Author

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


1. First-Order Differential Equations.
2. Mathematical Models and Numerical Methods.
3. Linear Equations of Higher Order.
4. Introduction to Systems of Differential Equations.
5. Linear Systems of Differential Equations.
6. Nonlinear Systems and Phenomena.
7. Laplace Transform Methods.

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