Simmons advocates a careful approach to the subject, covering such topics as the wave equation, Gauss's hypergeometric function, the gamma function and the basic problems of the calculus of variations in an explanatory fashions - ensuring that students fully understand and appreciate the topics. Special features include: showing the primary purpose of differential equations to serve as a tool for the study of change in the physical world, by the many applications to science and mathematics itself; and allowing students to grasp the nature and significance of the subject, while maintaining a mathematical rigor. Many biographical notes are provided to convey to students a sense of the history of the subject.
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. The Calculus of Variations. The Existence and Uniqueness of Solutions. Numerical Methods. Numerical Tables. Answers.