Lectures related to Construction of Measures: Separation and Partition

Explores compact sets, extreme values, and function theorems on bounded sets.

Limits of Functions in Several Variables

Explores limits of functions in several real variables, including the two gendarmes theorem and the minimum and maximum theorem on compact sets.

Maximum and Minimum of Functions

Explores limits, minimum and maximum values of functions, and continuity criteria in a compact set.

Optimization of Functions: Maximum and Minimum

Covers the optimization of functions, focusing on finding the maximum and minimum values over a given domain.

Optimization: Extrema of Functions

Covers the optimization of functions, focusing on finding the maximum and minimum values.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Limit of Functions: Convergence and Boundedness

Explores limits, convergence, and boundedness of functions and sequences.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Limits of Multivariable Functions: Techniques and Theorems

Discusses limits of multivariable functions, focusing on definitions, examples, and techniques for calculating limits effectively.

Initial Problem Solutions

Covers the description of problem solutions and the concept of compactness and uniform continuity.

Optimal Transport: Analysis and Proofs

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.

Distribution Interpolation Spaces

Covers distribution interpolation spaces, including the regularized flux and extension operators.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Understanding Microcontrollers: Functions

Introduces the fundamentals of functions in microcontroller programming, emphasizing naming rules and step-by-step development.

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

Approximation by Smooth Functions

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Continuity of Functions: Definitions and Notations

Explores the continuity of functions in R² and R³, emphasizing accumulation points and limits.