Lectures related to Differentiability: Continuous Strictly Monotone Functions

Linear Algebra Fundamentals

Explores linear algebra fundamentals, including key definitions, theorems, and practical applications in mathematics and technology.

Extreme Values of Continuous Functions

Covers extreme values of continuous functions on compact sets and differentiability.

Derivability and Maximum Values

Covers the theorem of intermediate values and finding maximum and minimum values of functions on closed intervals.

Intermediate value theorem

Explores uniform continuity, Lipschitz functions, and the intermediate value theorem with examples and proofs.

Derivability and Chain Rule

Covers the demonstration of the chain rule and the theorem of Rolle.

Fubini's Theorem: Multiple Integrals

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

Intermediate Value Theorem

Covers the Intermediate Value Theorem and its applications in finding solutions of equations and understanding the properties of continuous functions.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Continuous Functions: Theory and Applications

Explores continuous functions, Cauchy criterion, and function extension by continuity.