Differential Equations with Applications and Historical Notes, 3rd Edition

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. A solutions manual is available upon qualifying course adoption.

• 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

Solutions manual available upon qualifying course adoption

Table of Contents

Chapter 1: The Nature of Differential Equations. Separable Equations
Chapter 2: First Order Equations
Chapter 3: Second Order Linear Equations
Chapter 4: Qualitative Properties of Solutions
Chapter 5: Power Series Solutions and Special Functions
Chapter 6: Fourier Series and Orthogonal Functions
Chapter 7: Partial Differential Equations and Boundary Value Problems
Chapter 8: Some Special Functions of Mathematical Physics
Chapter 9: Laplace Transforms
Chapter 10: Systems of First Order Equations
Chapter 11: Nonlinear Equations
Chapter 12: The Calculus of Variations
Chapter 13: The Existence and Uniqueness of Solutions
Chapter 14: Numerical Methods