Asymptotic Theory -- Made Easy

Ram P. Kanwal
Department of Mathematics
Penn State

Abstract:

This lecture synthesizes three branches of APPLIED MATHEMATICS:

  1. ASYMPTOTIC ANALYSIS
  2. GENERALIZED FUNCTIONS
  3. THE THEORY OF MOMENTS
First we give a brief review of basic results of Generalized functions as needed in our presentation. Then we introduce the concepts of moments. This helps us to derive the asymptotic expansion formula given by Estrada and Kanwal. After that we present various celebrated results of the Asymptotic Analysis, such as the evaluation of oscillatory integrals. The lecture ends with the solution of the telegraph equation. In addition to using various concepts mentioned above, this solution helps us to introduce some more items such as the dispersive wave.