Lectures related to Analysis I: Decreasing and Growing Functions

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Explores compact sets, extreme values, and function theorems on bounded sets.

Explains how to find local extrema of functions using derivatives and critical points.

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Covers the composition of piecewise functions and introduces the signum and Heaviside functions.

Covers functions, including even and odd functions, periodicity, and function operations.

Covers limits at infinity, algebra, and continuity with examples.