Lectures related to Stability of fixed points

Newton's Method: Convergence and Criteria

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Linear Systems in 2D: Stability

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

Dynamic Systems: Formalism and Bases

Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.

Fixed Points and Stability

Explores fixed points and their stability in dynamic systems, emphasizing linear stability analysis.

Dynamic Systems: Course Review

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Phase Portraits and Predator-Prey Models

Explores phase portraits in 2D systems and the dynamics of predator-prey models.

Physics Mini-Test: Trajectory Analysis

Explores the analysis of a ball's trajectory in contact with a beam, focusing on forces, angles, and motion equations.

Stability Analysis: Linear Systems

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Linear Algebra: Systems of Linear Equations

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

Fixed Point Methods: Non-linear Equations

Covers fixed point methods for finding zeros of non-linear equations.

Nonlinear Dynamics: Stability and Chaos

Explores fixed point stability, Lyapunov functions, Lotka-Volterra models, and nonlinear dynamics in complex systems.

Numerical Analysis: Nonlinear Equations

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Discrete Time Solution: Stability Properties and Fixed Points

Explores stability properties and fixed points in discrete time solutions.

Stationary Distribution in Markov Chains

Explores the concept of stationary distribution in Markov chains, discussing its properties and implications, as well as the conditions for positive-recurrence.

Numerical Analysis: Newton's Method

Explores Newton's method for finding roots of nonlinear equations and its interpretation as a second-order method.

Non-linear Equations and Systems

Addresses solving non-linear equations and systems numerically using fixed point and Newton's methods.

Scaling & Renormalization in Statistical Mechanics

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Canonical Analysis: Quadratic Geometry

Explores canonical analysis of quadratic functions to identify conic shapes in planes.