Lectures related to Projected Gradient Descent: Quadratic Penalty

Advanced Analysis 2: Continuity and Limits

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

Solving Equations: Newton's Method

Covers Newton's method conditions and convergence, extension to multiple variables, and linear models.

Optimization Methods

Covers optimization methods without constraints, including gradient and line search in the quadratic case.

Differential Equations: Solutions and Periodicity

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

Newton Method: Convergence and Quadratic Care

Covers the Newton method and its convergence properties near the optimal point.

Continuous Functions: Criteria and Equivalences

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

Function Approximations

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

Distribution Interpolation Spaces

Covers the proof of UE Lipschitz constant and distribution interpolation spaces.

Distribution to Spaces: Interpolation and Continuity

Covers weak derivatives, interpolation spaces, and continuity in function spaces.

Advanced Analysis I: Continuous Functions on Compact Sets

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

Bolzano-Bastra-Sterl: Applications and Uniform Continuity

Explores the Bolzano-Bastra-Sterl theorem and uniform continuity in sequences.

Generalized Integrals: Type 2

Covers the integration of limit expansions and continuous functions by pieces.

Limits and Continuity: Analysis 1

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

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.

Intermediate Value Theorem

Covers the Intermediate Value Theorem, uniform continuity, Lipschitz functions, and the properties of continuous functions.

Real Functions: Continuity Extension

Discusses extending a function uniformly and its continuity properties in real functions.

Vector Spaces and Convergence

Covers vector spaces, compact sets, convergence, continuity, and uniqueness theorems.

Uniform Continuity: Definitions and Examples

Explores uniform continuity in functions, covering definitions, examples, and properties.

Gradient Descent: Lipschitz Continuity

Explores Lipschitz continuity in gradient descent optimization and its implications on function optimization.

Multiple Integration: Fubini Theorem

Explores multiple integration in R², focusing on double integrals over closed rectangles and the Fubini theorem.