AST 557 - Analytical Techniques in Differential Equations

This class covers topics of asymptotic methods and their applications. These include dominant balance, approximate solutions of differential equations, Frobenius expansions and divergent asymptotic expansions depending on type of singularities, complex integral representations & asymptotic integral evaluations through steepest descent path, saddle points, Stokes phenomena in analytic continuation, using the examples of special functions such as Airy, Gamma, Bessel, Parabolic Cylinder, Riemann-Zeta functions. This leads us to discuss WKB theory and applications to physics problems such as bound eigenstates and wave transmissions.

Steven Cowley, Jong-Kyu Park

Fall 2022, Fall 2021, Fall 2020, Fall 2019, Fall 2018

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