This note
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.
This note
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.