Morse Theory: Critical Points and Non-Degeneracy

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

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

Explores volume calculation for spheres, function definition, and loop logic.

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

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

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

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