This course covers the fundamentals of distribution theory, including the motivation behind distributions, test functions, convergence for test functions, the space of distributions, regular distributions, and the properties of the delta distribution. Students will learn about the vector space formed by distributions, multiplication with smooth functions, and coordinate transformations. The course aims to equip learners with a solid understanding of distribution theory and its applications. The intended audience for this course includes mathematics students, researchers, and professionals seeking to deepen their knowledge in advanced mathematical concepts.
Overview
Syllabus
Distributions Part 1: Motivation and delta function.
Distributions Part 2: Test functions.
Distributions Part 3: Convergence for test functions.
Distributions Part 4: Space of distributions.
Distributions Part 5: Regular Distributions.
Distributions Part 6: The Delta Distribution is not regular.
Distributions Part 7: Distributions form a Vector Space.
Distributions Part 8: Multiplication with Smooth Functions.
Distributions Part 9: Coordinate Transformations.
Taught by
The Bright Side of Mathematics
