Lectures related to Counting: Basic Principles and Applications

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

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

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

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

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

Introduces sets, functions, and proofs in mathematics, covering set equality, subsets, Cartesian products, and truth sets of predicates.

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

Covers the basic concepts of sets, functions, and number systems.

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

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

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

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

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

Covers weak derivatives, their properties, and applications in functional analysis.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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

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

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

Explores continuous functions and integrability through practical examples.

Covers the concept of continuity of functions and determining continuity at specific points through examples.