Advanced Analysis I: Uniform Convergence

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Page 2 of 3

Advanced Analysis 2: Continuity and Limits

Delves into advanced analysis topics, emphasizing continuity, limits, and uniform continuity.

Limits and Continuity in Multivariable Functions

Covers limits and continuity in multivariable functions, including examples and techniques for showing the existence of limits.

Convergence and Limits in Real Numbers

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Calculus of Variations: Principles and Applications

Explores the principles and applications of calculus of variations, focusing on uniform boundedness and equi-integrability of Carathéodory integrands.

Limit and Function Composition

Covers the concept of limit at a point and function composition in the context of continuous functions.

Generalized Integrals: Bounded Interval

Introduces generalized integrals on a bounded interval, discussing convergence, divergence, comparison criteria, variable substitution, and corollaries.

Interpolation of a Continuous Function

Explores the interpolation of a continuous function by a polynomial.

Generalized Integrals: Elementary Cases

Explores elementary cases of generalized integrals, convergence criteria, and the interpretation of integrals of type i and ii.

Limit of Functions: Convergence and Boundedness

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

Continuous Functions: Criteria and Equivalences

Explores criteria for continuity, convergence of sequences, and equivalence conditions for continuous functions.