Distribution Theory

Dive into a comprehensive 1.5-hour video lecture on distribution theory presented by The Bright Side of Mathematics. Explore the foundations of this mathematical concept, starting with the motivation behind distributions and the delta function. Progress through the intricacies of test functions, convergence, and the space of distributions. Examine regular distributions and understand why the Delta Distribution is not considered regular. Learn about the vector space properties of distributions, their multiplication with smooth functions, and coordinate transformations. Gain a thorough understanding of this advanced mathematical topic through clear explanations and step-by-step demonstrations.

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.