Differential Equations: A First Course

This comprehensive text suitable for math, science, and engineering majors, treats standard elementary topics such as undetermined coefficients, systems of differential equations, substitutions and chemical reactions. Students benefit from the conceptual approach, motivated by detailed physical and mathematical examples. Previous exposure to linear algebra or vectors is not assumed: all necessary linear algebra techniques are introduces as needed with respect to systems of differential equations. Early and consistent notation emphasizes the characteristic polynomial, suggests shortcuts such as the exponential shift, and leads to a natural, unified understanding of undetermined coefficients. Expanded treatment of the qualitative theory of linear systems, especially as applied to nonlinear systems, includes new sections on Interacting Populations, Constants of Motion, Lyapunov Functions, and Limit Cycles and Chaos. BASIC computer programs on approximation algorithms illustrate the use of technology in numerical methods.