Lectures related to Hölder condition

Introduces Le spaces, measurable functions, Holder inequality, and LP space properties.

Covers key concepts in nonlinear dynamical systems, such as existence, uniqueness, and continuous dependence of solutions.

Covers the bisection method proposition and its demonstration for finding roots.

Explores Lipschitz conditions in differential equations and their implications on solutions and properties.

Explores the Lipschitz condition for functions and its implications on the uniqueness of solutions to the Cauchy problem.

Covers the proof of UE Lipschitz constant and distribution interpolation spaces.

Explores the existence and uniqueness theorem of maximal solutions to Cauchy problems within specific intervals.

Explains how a function reaches its maximum and minimum values.

Introduces Riemann sums as approximations of the area under a function's graph.

Covers integration by change of variables and the derivation in chain rule.

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

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

Explores the interpolation of a continuous function by a polynomial.

Covers weak derivatives, interpolation spaces, and continuity in function spaces.

Explains the definition and uniqueness of developments limites for continuous functions on open intervals.

Explores the integral change of variable formula and its applications in calculus.

Explores the integral part of the Fundamental Theorem of Analysis with examples like y = cos(x).

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

Covers finding unique local maxima and functions oscillating infinitely.

Covers the Theoreus Chain Role for Lipschitz functions and its practical applications.