Differential Equations with Applications and Historical Notes

Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations―among others―as an undergraduate, then he/she is unlikely to do so later.

The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author―a highly respected educator―advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter.

With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity―i.e., identifying why and how mathematics is used―the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout.

• Provides an ideal text for a one- or two-semester introductory course on differential equations
• Emphasizes modeling and applications
• Presents a substantial new section on Gauss’s bell curve
• Improves coverage of Fourier analysis, numerical methods, and linear algebra
• Relates the development of mathematics to human activity―i.e., identifying why and how mathematics is used
• Includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout
• Uses explicit explanation to ensure students fully comprehend the subject matter

Outstanding Academic Title of the Year, Choice magazine, American Library Association.

Table of Contents

1: The Nature of Differential Equat ions. Separable Equations

2: First Order Equations

3: Second Order Linear Equations

4: Qualitative Properties of Solutions

5: Power Series Solutions and Special Functions

6: Fourier Series and Orthogonal Functions

7: Partial Differential Equations and Boundary Value Problems

8: Some Special Functions of Mathemat ical Physics

9: Laplace Transforms

10: Systems of First Order Equations

11: Nonlinear Equations

12: The Calculus of Variations

13: The Existence and Uniqueness of Solutions

14: Numerical Methods

About the Author

George F. Simmons has academic degrees from the California Institute of Technology, Pasadena, California; the University of Chicago, Chicago, Illinois; and Yale University, New Haven, Connecticut. He taught at several colleges and universities before joining the faculty of Colorado College, Colorado Springs, Colorado, in 1962, where he is currently a professor of mathematics. In addition to Differential Equations with Applications and Historical Notes, Third Edition (CRC Press, 2016), Professor Simmons is the author of Introduction to Topology and Modern Analysis (McGraw-Hill, 1963), Precalculus Mathematics in a Nutshell (Janson Publications, 1981), and Calculus with Analytic Geometry (McGraw-Hill, 1985).