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

The Nature of Differential Equations: Separable Equations. First-Order Equations. Second-Order Linear Equations. Qualitative Properties of Solutions. Power Series Solutions and Special Functions. Fourier Series and Orthogonal Functions. Partial Differential Equations and Boundary Value Problems. Some Special Functions of Mathematical Physics. Laplace Transforms. Systems of First-Order Equations. Nonlinear Equations. Calculus of Variations. The Existence and Uniqueness of Solutions. Numerical Methods. Numerical Tables.