Lectures related to Brouwer fixed-point theorem

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

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

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

Explores the convergence of fixed point methods and the implications of different convergence rates.

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

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Explores the local inversion theorem, demonstrating uniqueness of solutions and continuity of functions.

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

Introduces the fixed point method for solving nonlinear equations by transforming the problem into an equivalent form.

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

Explores applying fixed point methods to solve electrical circuit equations and find diode voltage.

Covers fixed point methods and the Picard method for solving nonlinear equations iteratively.

Explores nonlinear equations, bisection, fixed-point methods, error control, and graphical interpretations of fixed points.

Covers the fixed point method for solving nonlinear equations and discusses convergence properties.

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

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

Explores the global convergence of the fixed point method for nonlinear equations.

Explores Lipschitz dependence supported by examples and theoretical hypotheses, emphasizing global unique solutions.

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

Covers fixed-point methods and Newton-Raphson, emphasizing their convergence and error control.