Lectures related to Closed Intervals: Definitions and Remarks

Explores Rolle's Theorem for continuous and differentiable functions on closed intervals.

Covers Rolle's Theorem and the Mean Value Theorem with illustrative examples.

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Explores finding the equation of the tangent line to a function's graph at a point.

Explains partial derivatives, Hessienne matrix, and their properties.

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Covers the definition of differentiable functions and explores the representation of the remainder in derivatives.

Covers the definition of derivatives and provides examples of differentiable functions.

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Explores the extension of the chain rule to higher dimensions and compositions of functions.

Explores Taylor series expansions for derivatives and integrals, including practical applications.

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Explores algebraic operations on limited developments and their consequences on differentiable functions, illustrated through examples.

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Revisits the definition of differentiability and the existence of derivatives for functions in open intervals.

Covers the concept of approximating a function around a point xo using linear approximation.

Covers differentiable functions, derivatives, and tangent planes in mathematics.