Written in a clear, precise and readable manner, this textbook (now revised and corrected) is designed to provide postgraduate mathematics students with a sound and inspiring introduction to the main themes of ordinary differential equations. It is presented from the viewpoint of applied mathematics to treat differential equations both from the theoretical background and practical applications to scientific and engineering problems.
Beginning with a comprehensive treatment of linear differential equations with variable coefficients, the text gives a detailed discussion on some well-known special functions which provide solutions of secondorder linear ordinary differential equations having several regular singular points. Many of the standard concepts and methods which are useful in the study of special functions are discussed. The properties of special functions are derived from their differential equations and boundary conditions. Finally, existence and uniqueness of solutions of differential equations are established.
Worked-out examples are introduced throughout the text. End-of-chapter exercises further help understand the mathematical and physical structure of the subject.