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This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic, hyperbolic and parabolic differential operators, a method of characteristics. In addition to that review of Lebesgue integration, distributions, Fourier transform, homogeneous distributions and asymptotic methods will also be discussed in this course. If students are interested in this course then this course is the perfect one.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: MIT

Course Curriculum

Module: 01
Continuous Functions 00:15:00
Measures and σ-algebras 00:10:00
Measureability of Functions 00:05:00
Integration 00:20:00
Hilbert Space 00:05:00
Module: 02
Test Functions 00:15:00
Tempered Distributions 00:10:00
Convolution and Density 00:20:00
Fourier Inversion 00:10:00
Sobolev Embedding 00:05:00
Differential Operators 00:30:00
Module: 03
Cone Support and Wavefront Set 00:20:00
Homogeneous Distributions 00:05:00
Spectral Theorem 00:05:00
Problems 01:00:00
Solutions 00:10:00
References 00:05:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

Course Reviews

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