Stability of fixed points

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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.