3 Review(s)

"This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering, and biology. The text begins with a coverage of ordinary differential equations. The concepts of first- and second-order equations are covered at first. It moves further to include concepts of linear systems, series solutions, regular Sturm-Liouville theory, boundary value problems, and qualitative theory. Thereafter, partial differential equations are covered. First-order partial differential equations, classification of partial differential equations, and Laplace and Poisson equations are also discussed in detail. The book concludes with a coverage on heat equation, one-dimensional wave equation and wave equation in higher dimensions. It highlights the importance of analysis, linear algebra, and geometry in the study of differential equations, including some multiple characteristics problems. It provides sufficient theoretical material at the beginning of each chapter which will enable students to better understand the concepts and begin solving problems straightaway.KEY FEATURES•Chapter-wise exercises with their solutions •Includes problems from traditional topics as well as control theory and kinematics•Includes the local version of potential theory and Widder’s uniqueness result of positive solutions of the heat equation•Includes a coverage on multiple characteristic problems for hyperbolic equations and systems"