NOC:Advanced Partial Differential Equations (Part I: Distributions and Sobolev Spaces)

Lecture 1 - Introduction - 1

Lecture 2 - Preliminaries - 1

Lecture 3 - Preliminaries - 2

Lecture 4 - Priliminaries - 3

Lecture 5 - Priliminaries - 4

Lecture 6 - Preliminaries - 5

Lecture 7 - Prelimunaries - 6

Lecture 8 - Preliminaries - 7

Lecture 9 - Preliminaries - 8

Lecture 10 - Preliminaries - 9

Lecture 11 - Introduction to Distributions

Lecture 12 - Properties and Examples

Lecture 13 - Convergence of distributions

Lecture 14 - Convergence of distributions

Lecture 15 - Calculus in the space of distributions

Lecture 16 - Further discussion on Distributions

Lecture 17 - Order and support of a distribution

Lecture 18 - Laplace and Poisson equations - Distributions with compact support

Lecture 19 - Validity of the definition of the support

Lecture 20 - Convolution and Fourier transform of distributions

Lecture 21 - The Schwartz space andAKN Lec 15 its dual

Lecture 22 - Fourier transform of a tempered distribution, convolution

Lecture 23 - Properties of Convolution

Lecture 24 - Further discussion on Fourier transform and convolution

Lecture 25 - Convolution of two distributions

Lecture 26 - Convolution of distributions

Lecture 27 - Introduction to Sobolev spaces

Lecture 28 - Properties of Sobloev Spaces

Lecture 29 - Extension and Density results

Lecture 30 - General Extension result

Lecture 31 - Integration on a smooth surface

Lecture 32 - A more general extension result

Lecture 33 - Notion of the trace

Lecture 34 - A compactness theorem

Lecture 35 - Equivalent norms

Lecture 36 - Sobolev lemma

Lecture 37 - Sobolev lemma (Continued...)

Lecture 38 - Analysis near the boundary

Lecture 39 - Trace in the upper half space

Lecture 40 - Trace in the upper half space

Lecture 41 - Supplementary lecture

Lecture 42 - Supplementary lecture