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Analytical Techniques in Differential Equations

APC 503/AST 557

1232
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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.
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Section L01