Convolution of Distributions and Differential Equations

This lecture delves into the convolution of tempered distributions, exploring the definition and properties of this operation, as well as its application to linear filters. The instructor explains how to define the convolution product in the space of tempered distributions and illustrates its significance through examples involving the Dirac functional. Additionally, the lecture covers solving differential equations with tempered distributions, highlighting the fundamental solution concept and its role in obtaining solutions for equations with various input functions. The instructor concludes by emphasizing the importance of mastering these topics for future engineering studies and exams.