Lectures related to Contraction mapping

Fixed Point Theorem

Explores fixed point theorems, recurrent sequences, and convergence properties, emphasizing the significance of fixed points in analysis.

Homogeneous Equations: Advanced Analysis II

Explores second-order linear scalar homogeneous equations in advanced analysis II.

Picard Method: Fixed Point Iterative Technique

Covers the Picard method for solving nonlinear equations using fixed point iteration.

Fixed Point Method: Global Convergence

Explores the fixed point method for global convergence in solving nonlinear equations.

Local Inverse Theorems

Covers the local inverse theorem, diffeomorphisms, contraction mappings, and the Jacobian determinant.

The Banach Fixed Point Theorem

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Advanced Analysis II: Homogeneous ODEs and Banach Spaces

Explores the resolution of ODEs and the Banach fixed-point theorem.

Linear Hatching Systems: Unique Solutions and Norm Introduction

Explores linear hatching systems, unique solutions, norms, and fixed points in linear systems.

Fixed Point Theorem: Convergence of Newton's Method

Covers the fixed point theorem and the convergence of Newton's method, emphasizing the importance of function choice and derivative behavior for successful iteration.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Obstacle Avoidance with DS

Explores obstacle avoidance using Dynamical Systems for robots, focusing on modulation, stability guarantees, and contraction theory.

Normal Ordered Product And Wick Theorem

Covers normal ordered product, Wick's theorem, creation and destruction fields, and efficient computation methodology.

Accelerated Algorithms for Monotone Inclusions

By Quoc Tran-Dinh explores accelerated algorithms for monotone inclusions, covering optimization models, challenges, and new algorithms.

Stochastic Differential Equations

Explores Stochastic Differential Equations, discussing existence, uniqueness, Lipschitz properties, and explicit solutions.

Differential Equations: Existence and Uniqueness Theorems

Covers the existence and uniqueness of solutions for differential equations.

Quantum Mechanics: Hartree-Fock Method

Covers the Hartree-Fock method and second quantization in quantum mechanics for systems with multiple particles.

Lipschitz Maps and Compact Domains

Covers Lipschitz maps, compact domains, changing variables, counting problems, and probability of ideals.