About the Author

Professor Roscoe White is a Principal Research Physicist at the Princeton Plasma Physics Laboratory, where he was head of the theory division for six years. He graduated in Physics from the University of Minnesota and then obtained his Ph.D. in Physics from Princeton. He is a fellow of the American Physics Society and has published over 250 articles and one book in the areas of fusion physics and nonlinear dynamics.

An essential graduate level text on the asymptotic analysis of ordinary differential equations, this book covers all the important methods including dominant balance, the use of divergent asymptotic series, phase integral methods, asymptotic evaluation of integrals, and boundary layer analysis. The construction of integral solutions and the use of analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. There is no attempt to give a complete presentation of all these functions. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.

Contents:

• Dominant Balance
• Exact Solutions
• Complex Variables
• Local Approximate Solutions
• Phase Integral Methods
• Perturbation Theory
• Asymptotic Evaluation of Integrals
• The Euler Gamma Function
• Integral Solutions
• Expansion in Basis Functions
• Airy
• Bessel
• Weber– Hermite
• Whittaker and Watson
• Inhomogeneous Differential Equations
• The Riemann Zeta Function
• Boundary Layer Problems

“This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and physicists who require an introduction to asymptotic techniques.”