Differential Equations for Engineers

Xie presents a systematic introduction to ordinary differential equations for engineering students and practitioners. Mathematical concepts and various techniques are presented in a clear, logical, and concise manner. Various visual features are used to highlight focus areas. Complete illustrative diagrams are used to facilitate mathematical modeling of application problems. Readers are motivated by a focus on the relevance of differential equations through their applications in various engineering disciplines. Studies of various types of differential equations are determined by engineering applications. Theory and techniques for solving differential equations are then applied to solve practical engineering problems. A step-by-step analysis is presented to model the engineering problems using differential equations from physical principles and to solve the differential equations using the easiest possible method. This book is suitable for undergraduate students in engineering.

1. Introduction; 2. First-order and simple higher-order differential equations; 3. Applications of first-order and simple higher-order equations; 4. Linear differential equations; 5. Applications of linear differential equations; 6. The Laplace transform and its applications; 7. Systems of linear differential equations; 8. Applications of systems of linear differential equations; 9. Series solutions of differential equations; 10. Numerical solutions of differential equations; 11. Partial differential equations; 12. Solving ordinary differential equations using Maple; Appendix A. Tables of mathematical formulas.

Wei-Chau Xie is a Professor in the Department of Civil and Environment Engineering and the Department of Applied Mathematics at the University of Waterloo. He is the author of Dynamic Stability of Structures and has published numerous journal articles on dynamic stability, structural dynamics and random vibration, nonlinear dynamics and stochastic mechanics, reliability and safety analysis of engineering systems, and seismic analysis and design of engineering structures. He has been teaching differential equations to engineering students for almost twenty years. He received the Teaching Excellence Award in 2001 in recognition of his exemplary record of outstanding teaching, concern for students, and commitment to the development and enrichment of engineering education at Waterloo. He was the recipient of the Distinguished Teacher Award in 2007, which is the highest formal recognition given by the University of Waterloo for a superior record of continued excellence in teaching.