Lectures related to Numerical methods for linear least squares

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

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

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

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

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

Covers Richardson extrapolation for numerical differentiation to reduce error.

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

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

Explores backward and central differences for numerical differentiation, analyzing their properties and error analysis.

Explores inference for stochastic differential equations, focusing on numerical methods and convergence analysis.

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

Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.

Introduces the Euler Forward Method for ODEs, focusing on error analysis and stability.

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

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

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

Explores direct methods for solving linear systems of equations, including Gauss elimination and LU decomposition.

Explains Galerkin orthogonality in numerical methods and its stability criteria.

Covers band matrices, linear systems, stability analysis, and boundary corrections in numerical methods.

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