Notes, Problems and Solutions in Differential Equations

This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems, series solutions, regular Sturm–Liouville theory, boundary value problems and qualitative theory. Thereafter, partial differential equations are explored. Topics such as first-order partial differential equations, classification of partial differential equations and Laplace and Poisson equations are also discussed in detail. The book concludes with 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. 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.

• Chapter-wise exercises with solutions
• Includes problems from traditional topics as well as from 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 of multiple characteristics problems for hyperbolic equations and systems