Lectures related to Optimization: Extrema of Functions

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

Covers the method of Lagrange multipliers to find extrema subject to constraints.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

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

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Demonstrates the practical application of theorems in calculus through two clever examples.

Explores continuous functions and integrability through practical examples.