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.
contains the following subcategories, Continuous Functions , Measures and
algebras , Measureability of Functions, Integration, Hilbert Space, Test
Functions, Tempered Distributions , Convolution and Density, Fourier Inversion,
Sobolev Embedding , Differential Operators , Cone Support and Wavefront Set,
Homogeneous Distributions and Spectral Theorem.
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: fundamental
solutions for elliptic, hyperbolic and parabolic differential operators, method
of characteristics, review of Lebesgue integration, distributions, fourier
transform, homogeneous distributions, asymptotic methods.
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.