Lectures related to Taylor Expansion and Convex Functions

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Taylor's approximation: Analysis & Applications

Covers Taylor's approximation theorem, differentiability, error control, and function expansions.

Proximal and Subgradient Descent: Optimization Techniques

Discusses proximal and subgradient descent methods for optimization in machine learning.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Optimization Techniques: Gradient Descent and Convex Functions

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.

Functions Extension and Taylor Expansion

Covers functions extension and Taylor expansion, exploring mathematical concepts in depth.

Convexity: Functions and Global Minima

Explores convex functions, global minima, and their relationship with differentiability.

Functions: Limits and Continuity

Explores functions, limits, continuity, differentiability, and important notions of limits and divergence.

Optimization Basics: Norms, Convexity, Differentiability

Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Generalized Integrals: Type 2

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

Darboux Theorem: Advanced Analysis I

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Continuous Functions: Definitions and Continuity Criteria

Explains continuous functions, criteria for continuity, and continuity concepts at points and intervals.

Limit and Function Composition

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

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Taylor Polynomials: Calculating Limits and Derivatives

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Limits and Continuity: Analysis 1

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

Convex Optimization: Gradient Descent

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Taylor Polynomials: Approximating Functions

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing functions.

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.