NOC:Advanced Partial Differential Equations (Part I: Distributions and Sobolev Spaces)
Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. P.S. Datti, Prof. A K Nandakumaran
NPTEL Co-ordinating Institute : IISc Bangalore
NPTEL Lecture Count : 42
NPTEL Course Size : 4.0 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
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