"This book was written for advanced undergraduate math or science majors. Its initial purpose was to illustrate the elementary mathematical theory of ordinary differential equations and their diverse and powerful applications. Historically these have been decisive in many physical problems, some of which have philosophically challenged and indeed altered our civilization's concepts. Because of the importance of the subject, the book is also suitable for a one-semester course for graduate students. The book consists of 12 chapters and six appendices. Contents: First Order Equations and Introduction to Ordinary Differential Equations; Planetary Motion.I; Second Order Ordinary Differential Equations; Some More Advanced Topics in ODEs; Approximation of Solutions; Minding's and Sturm's Theorems; Two by 2 Linear Systems; Autonomous Dynamical Systems and the Poincare-Bendixson Theorem; Matrix Differential Equations and the Matrix Exponential Function; Classical Partial Differential Equations of the Second Order; An Introduction to the Calculus of Variations; The Gauss Bonnet Theorem for Surfaces; Appendices: The Gaussian Distribution; Contraction Mappings and Picard's Existence Theorem; Stokes' Theorem; Real Analytic Functions; Fourier Series; Special Relativity;"-- Provided by publisher.
