Lectures related to Newton's Method: Convergence and Quadratic Convergence

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Taylor Series: Convergence and Applications

Explores Taylor series development, convergence criteria, and numerical applications.

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

Newton Method: Convergence and Quadratic Care

Covers the Newton method and its convergence properties near the optimal point.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Fixed-Point Methods and Newton-Raphson

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

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.

Iterative Methods for Nonlinear Equations

Explores iterative methods for solving nonlinear equations, discussing convergence properties and implementation details.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Convergence of Fixed Point Methods

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

Newton's Method: Order 2

Explains Newton's method of order 2 for finding function zeros.

Digital Physics: Convergence and Error Analysis

Discusses evaluation feedback, convergence, error analysis, and adaptive time steps in physics simulations.

Numerical Methods: Stopping Criteria, SciPy, and Matplotlib

Discusses numerical methods, focusing on stopping criteria, SciPy for optimization, and data visualization with Matplotlib.

Newton's Method: Graphical Approach

Illustrates the Newton's method graphically, discussing convergence and extreme cases.

Newton Method: Convergence Analysis

Explores the Newton method for root finding and its convergence analysis, including the modified Newton method.

Numerical Methods in Physics

Covers numerical methods in physics, focusing on solving complex problems and understanding limitations.

Numerical Methods: Iterative Techniques

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Convergence Analysis: Explicit RK Scheme

Explores the convergence analysis of the Explicit Runge-Kutta scheme for accurate numerical solutions.

Computational Geomechanics: Unconfined Flow Analysis

Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.

Newton's Method: Fixed Point Iterative Approach

Covers Newton's method for finding zeros of functions through fixed point iteration and discusses convergence properties.