The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painlevé functions. The volume is suitable for graduate students and researchers interested in differential equations and special functions.

Readership

Graduate students and research mathematicians interested in differential equations and special functions.

Table of Contents

• Borel resummation
• WKB analysis of Schrödinger equations
• Applications of WKB analysis to global problems
• WKB analysis of the Painlevé function
• Future directions and projects
• Appendix
• Bibliography
• Index