Maximum and Minimum of Functions

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Analysis I: Decreasing and Growing Functions

Explores decreasing and growing functions, bounded sequences, and limit existence.

Limits and Continuity: Analysis 1

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Real Functions: Definitions and Properties

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

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.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Optimal Transport: Analysis and Proofs

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

Advanced Analysis II: Integrals and Functions

Covers advanced topics in analysis, focusing on integrals, functions, and their properties.

Existence of y: Proofs and EDO Resolution

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Extreme Points and Compact Intervals

Covers extreme points, compact intervals, and optimization problems in analysis.