Advanced Analysis II: Derivatives and Functions

Related lectures (27)

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Covers derivatives, chain rule, and composed functions with examples and applications.

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

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

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

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

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Explores derivability and function composition with examples.

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.

Explores solutions of differential equations and their monotonicity properties.