Lectures related to Nonlinear Problem Solving

Numerical Methods: Iterative Techniques

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

Computational Geomechanics: Unconfined Flow

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

Attack on RSA using LLL

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

Numerical Methods in Chemistry

Covers the implementation of numerical methods in MATLAB for solving chemical problems.

Numerical Methods in Biomechanics: Hip-A

Explores numerical methods in biomechanics for hip implants and emphasizes understanding conditions for improved designs and patient outcomes.

Numerical Differentiation: Part 1

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

Neutron Diffusion Equation: Numerical Methods

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

Multigroup Theory: Main Equations and Numerical Solution

Covers the derivation of multi-group diffusion equations and the numerical methods for solving the neutron diffusion equation.

ODEs: Introduction and Solutions

Covers Ordinary Differential Equations, first-order solutions, and numerical methods for IVP and BVP.

Finite Elements: Elasticity and Variational Formulation

Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.

Sensitivity of Solutions

Explores the sensitivity of solutions in numerical methods, including linear systems and matrix norms, with an example of deblurring images.

Numerical Integration: Lagrange Interpolation, Simpson Rules

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.

Numerical Integration: Romberg Integration

Explores Romberg integration to improve numerical integration accuracy through iterative refinement of estimates.

Numerical Analysis: Introduction to Computational Methods

Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

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.

Nonlinear Equations: Bisection Method

Introduces root finding using the bisection method for nonlinear equations, illustrated with a three-tanks system example.

High Order Methods: Space Discretisation

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

Numerical Differentiation: Richardson Extrapolation

Covers Richardson extrapolation for numerical differentiation to reduce error.

Numerics: semester project

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

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.