Generalized functions and weak derivatives - A very brief introduction

This video gives a brief introduction into the ideas underlying generalized functions (aka distributions) and the weak derivatives we can take of them. The emphasis is on working out the ideas rather than mathematical rigor and generality. Sections 00:00 Greetings 03:06 1. Test functions and generalized functions 05:47 The space T* of generalized functions (distributions) 06:31 Embedding continuous functions in the dual space of the test functions 08:51 2. Weak derivatives 11:38 Weak derivatives for non-differentiable functions and linear functionals 13:42 3. Examples 14:02 Absolute value 18:21 Heaviside function 22:06 Dirac distribution #distributions #functionalanalysis #weak #derivatives #maths #mathematics #dirac #delta