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: 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.

The main goal of this course note is to give the students a
solid foundation in the theory of elliptic and parabolic linear partial
differential equations. It is the second semester of a two-semester,
graduate-level sequence on Differential Analysis.

This lecture note covers the following topics: Analysis In Banach
Spaces, The Method of Lyapunov Schmidt, Degree Theory, Global Solution Theorems,
Existence and Uniqueness Theorems, Linear Ordinary Differential Equations,
Periodic Solutions, Stability Theory, Invariant Sets, Hopf Bifurcation and
Sturm-Liouville Boundary Value Problems.