Differential Analysis Lecture notes by Richard B. Melrose

Differential Analysis Lecture notes by Richard B. Melrose

Differential Analysis Lecture notes by Richard B. Melrose

This
note covers the following topics: Measure and Integration, Hilbert spaces and
operators, Distributions, Elliptic Regularity, Coordinate invariance and
manifolds, Invertibility of elliptic operators, Suspended families and the
resolvent, Manifolds with boundary, Electromagnetism and Monopoles.

This note covers the following
topics: Introduction To PDE, Basic Tools of Analysis, Analysis of the Wave
Equation in Minkowski Space, Basic Concepts in Riemannian and Lorentzian
Geometry.

This lecture note covers the following topics: fundamental
solutions for elliptic, hyperbolic and parabolic differential operators, method
of characteristics, review of Lebesgue integration, distributions, fourier
transform, homogeneous distributions, asymptotic methods.