Lecture
This lecture covers the concept of piecewise continuous functions, defined as functions that are continuous over intervals but may have discontinuities at certain points. The instructor explains the definition and properties of these functions, providing examples and discussing their behavior. The lecture also delves into the classification of functions based on their continuity and the types of discontinuities they may exhibit, such as jump discontinuities. Various integral types, including improper integrals, are introduced and analyzed in the context of piecewise continuous functions.