Lectures related to Continuity of Functions

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

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

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

Covers the statement of the Bernoulli's Hospital Rule and its application.

Covers Morse theory, focusing on critical points and non-degeneracy.

Explores continuous functions and integrability through practical examples.

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

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

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

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

Presents the solution to finding the second-order Taylor polynomial of a function.

Explores real functions, covering parity, periodicity, and polynomial functions.

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

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

Discusses local extrema of functions in two variables around the point (0,0).

Covers advanced optimization methods using Lagrange multipliers to find extrema of functions subject to constraints.

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Covers level curves and graphs of functions in two and three dimensions.

Covers the concept of limits and explores limits at infinity with illustrative examples.