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.