Derivatives: Chain Rule and Composed Functions

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Advanced Analysis II: Derivatives and Functions

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

Implicit Functions Theorem

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

Integration by Substitution

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

Bernoulli's Hospital Rule

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

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Derivability and Composition of Functions

Explores derivability and function composition with examples.

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

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

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

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.