Differential Analysis II: Partial Differential Equations and Fourier Analysis
This MIT OpenCourseWare graduate course continues a two-part sequence on differential analysis, moving from elliptic partial differential equations with variable coefficients through to the minimal surface equation. It then turns to Fourier and harmonic analysis, with applications to combinatorics and number theory such as the Gauss circle problem, and to PDE theory through the Calderon-Zygmund inequality for the Laplacian and the Strichartz inequality for the Schrodinger equation. The final section covers solutions to the linear and non-linear Schrodinger equation. Throughout, the course emphasizes the technique of proving analytic estimates rather than just stating results. Materials include lecture notes and problem sets published freely through MIT OpenCourseWare, with no instructor interaction or certificate offered. The course assumes strong prior background in real analysis and PDE theory, consistent with its advanced graduate level.