Short description:

Designed for an introductory course on differential equations, this book uses explicit explanation to ensure students fully comprehend the subject matter. Emphasizing modeling and applications, the third edition of this classic text presents a substantial new section on Gauss?s bell curve and improves coverage of Fourier analysis, numerical meth

Long description:

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.

This is an attractive introductory work on differential equations, with extensive information in addition to what can be covered in a two-semester course. The order of the topics examined is slightly unusual in that Laplacians are covered after Fourier transforms and power series. The chapter on power series contains a section on hypergeometric equations, which could well be the first time that an introductory book on the subject goes that far. The book has plenty of exercises at the end of each section, and also at the end of each chapter. The solutions to some of these are included at the end of the book. Most chapters contain a few appendixes that are several pages long. Their subject is either related to the life and work of an exceptional mathematician (such as Newton, Euler, or Gauss) or pertains to an area of mathematics in which the theory of differential equations can be applied. The historical appendixes put the material in context, and explain which parts of the material were the most difficult to discover. The writing is pleasant and reader-friendly throughout. This work is an essential acquisition for all math libraries; no competing works have put the material in such a deep historical context.

--M. Bona, University of Florida

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.