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Differential Equations is a textbook on elementary differential equations. It educates the reader in not just theory, but methods and applications related to differential equations. Summary Of The Book Differential equations is a very important branch of modern mathematics which features prominent tools that help in solving problems in multiple fields such as physics, engineering, biology, and economics. From the days of its discovery, differential equations have been an important subject of research. For science, engineering, mathematics, and allied courses, differential equations hold great significance. The textbook Differential Equations gives its reader a thorough grounding in the subject. A student new to differential equations is first introduced to the fundamentals of ordinary differential equations. There lies the focus of the Part 1 of Differential Equations. It includes nine chapters, including Applications of Second-Order Linear Differential Equations with Constant Coefficients, Applications of First-Order Equations, Series Solutions of Linear Differential Equations, The Laplace Transform, and Approximate Methods of Solving First-Order Equations. In addition to a systematic introduction to fundamental theory, Part 2 introduces its readers to further methods and applications in differential equations. Part 2 includes topics like Existence and Uniqueness Theory, and Partial Differential Equations. The subject matter presented under these two parts include Linear Equations and Bernoulli Equations, Exact Differential Equations and Integrating Factors, Bessel’s Equation and Bessel Functions, Basic Theory of Linear Differential Equations, The Differential Equation of the Vibrations of a Mass on a Spring, Matrices and Vectors, Basic Theory of the Homogeneous Linear System, Sturm-Liouville Boundary-Value Problems, and Some Concepts from Real Function Theory. Appendices are provided at the end of the book to support the reader with any supplementary material he might need to solve the differential equations. Additionally, answers to the questions given in each chapter are provided, so that the students are able to verify their answers. About Shepley L. Ross Shepley L. Ross is an Associate Professor of Mathematics at Bates College. Other books authored by Shepley include Introduction to Ordinary Differential Equations. In 1985, Shepley joined the Mathematics department at Bates College. He has since taught courses on calculus, linear algebra, topology and abstract algebra. His favorite courses involve computational mathematics. His research focus is Dynamical Systems.