Lectures related to Calculus of Variations: Gradient Young Theorem

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Lipschitz Gradient Theorem

Covers the Lipschitz gradient theorem and its applications in function optimization.

Euler-Lagrange Equation

Explores the classical methods for solving optimization problems, emphasizing the Euler-Lagrange equation and its variants.

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Supremum Theorem

Explores the Supremum Theorem, its properties, proofs, and exercises.

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Gradient Descent Methods: Theory and Computation

Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.

Optimization with Constraints: Theory and Applications

Covers the theory and applications of optimization with constraints, including key concepts and numerical methods.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Inverse Function Identity

Explains the inverse function identity and provides examples with ln(x), sin(x), and cos(x).

Energy Systems Optimization

Explores energy systems modeling, optimization, and cost analysis for efficient operations.

Deep Learning Building Blocks

Covers tensors, loss functions, autograd, and convolutional layers in deep learning.

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.