Book 731


A thorough presentation of the methods for solving ordinary and partial differential equations, designed for undergraduates majoring in mathematics. The book includes detailed and well motivated explanations followed by numerous examples, varied problem sets, computer generated graphs of solutions and applications. The new edition expands its historical discussion and gives further emphasis on applications.

Brannan provides engineers with both an introduction to, and a survey of, modern methods, applications, and theory of a powerful mathematical apparatus that will help them in the field. Section exercises of varying levels of difficulty give them hands-on experience in modeling, analysis, and computer experimentation. New coverage is included on series solutions of second order linear equations, partial differential equations and Fourier Solutions, and boundary value problems and Sturm-Liouville Theory. The companion ODE Architect CD arms them with a user-friendly software tool for computing numerical approximations to solutions of systems of differential equations, and for constructing component plots, direction fields, and phase portraits. Physical representations of dynamical systems and animations available in the ODE Architect enable engineers to visualize solutions routinely.

Differential Equations: An Introduction to Modern Methods and Applications is a textbook designed for a first course in differential equations commonly taken by undergraduates majoring in engineering or science. It emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. Section exercises throughout the text are designed to give students hands--on experience in modeling, analysis, and computer experimentation. Optional projects at the end of each chapter provide additional opportunitites for students to explore the role played by differential equations in scientific and engineering problems of a more serious nature.