Lectures related to Solving Systems of Nonlinear Equations

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

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.

Numerical Derivation: Formulas and Approaches

Covers the numerical approach to derivative calculation, focusing on formulas and methods such as fine differences.

Newton's Method: Fixed Point Iterative Approach

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

Numerical Methods: Euler and Crank-Nicolson

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

Attack on RSA using LLL

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Numerical Analysis: Stability in ODEs

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

Crank-Nicolson and Heun's Methods

Covers the Crank-Nicolson and Heun's methods, discussing uniqueness of solutions and truncation errors in numerical methods.

Iterative Methods for Nonlinear Equations

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

Numerics: semester project

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

Thomas algorithm, accuracy of direct methods

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Energy System Optimization

Covers the optimization of energy systems, focusing on solving equations and numerical methods.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Nonlinear Equations: Methods and Applications

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

Neutron Diffusion Equation: Numerical Methods

Covers numerical methods for solving the neutron diffusion equation and addressing heterogeneous effects in thermal reactors.

Numerical Methods: Stopping Criteria, SciPy, and Matplotlib

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

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Root Finding Methods: Secant, Newton, and Fixed Point Iteration

Covers numerical methods for finding roots, including secant, Newton, and fixed point iteration techniques.