Lectures related to Sensitivity of Solutions

Thomas algorithm, accuracy of direct methods

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

Floating Point Numbers: LU Decomposition and Errors

Explores floating point numbers, LU decomposition, errors, and matrix properties.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

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 Differentiation: Part 1

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

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 Methods: Iterative Techniques

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

Numerical Derivation: Formulas and Approaches

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

Computational Geomechanics: Unconfined Flow

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

Direct Methods for Linear Systems of Equations

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

Numerical Modelling of the Atmosphere

Focuses on numerical modelling of atmospheric processes to predict weather and climate phenomena, covering key concepts and methods.

Numerical Methods in Chemistry

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

ODEs: Introduction and Solutions

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

Orthogonality and Least Squares Method

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

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.

Numerical Integration: Lagrange Interpolation, Simpson Rules

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

Numerical Differentiation: Backward and Central Differences

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

Stochastic Differential Equations: Mean-Field Inference

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

Numerical Differentiation: Richardson Extrapolation

Covers Richardson extrapolation for numerical differentiation to reduce error.

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.