Methods of Applied Mathematics II

The second half of the applied math methods sequence shifts from ODEs and finite-dimensional tools toward the continuous machinery you actually need for PDEs: variational principles, transform methods, and asymptotic analysis applied to the wave, heat, and Laplace equations. You'll spend the term working through problem sets out of Keener, classifying equations, deriving solutions via Riemann's method or integral transforms, and reasoning about stability, bifurcation, and inverse scattering on nonlinear problems. It's a graduate methods course meant to give applied math, physics, and engineering students a working toolkit for the PDEs that show up in research, building directly on MATH 543 and feeding into anything from fluid dynamics to mathematical physics.