Advanced Analysis 2: Continuity and Limits

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Differential Equations: Solutions and Periodicity

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

Advanced Analysis I: Continuous Functions on Compact Sets

Explores the necessity of uniform continuity for continuous functions on compact sets.

Limits and Continuity: Analysis 1

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

Continuous Functions: Criteria and Equivalences

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

Advanced Analysis II: Matrix Diagonalization

Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.

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.

Uniform Continuity: Limits, Series 8

Covers uniform continuity, one-sided limits, function behavior, and continuity conditions, with multiple-choice questions for practice.

Continuous functions on a closed bounded interval

Covers limits, range of continuous functions, and uniform continuity on closed intervals.

Preliminaries in Measure Theory

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

Function Approximations

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