Bolzano-Bastra-Sterl: Applications and Uniform Continuity

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Analysis IV: Convergence and Approximation in L² Space

Explores convergence and approximation in L² space, emphasizing the limitations of continuous functions and the importance of closed sets.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Limit of Functions: Convergence and Boundedness

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

Function Approximations

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Compact Subsets of R^n

Explores compact subsets of R^n, convergence theorems, and set properties.

Advanced Analysis 2: Continuity and Limits

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

Subsequences and Bolzano-Weierstrass Theorem

Covers the proof of the Squeeze Theorem, Quotient Criteria, and the Bolzano-Weierstrass Theorem.

Existence of Solutions for Poisson-Dirichlet Problem

Covers the existence of solutions for the Poisson-Dirichlet problem, focusing on showing that certain conditions hold for locally bounded and Hölder continuous functions.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.