Lectures related to Numerical Derivative

Numerical Differentiation: Backward and Central Differences

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

ODEs: Introduction and Solutions

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

Euler Forward Method

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

Numerical Differentiation: Part 1

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

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Energy System Optimization

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

Root Finding Methods: Bisection and Secant Techniques

Covers root-finding methods, focusing on the bisection and secant techniques, their implementations, and comparisons of their convergence rates.

Numerical Differentiation and Integration

Explores numerical differentiation and integration methods, emphasizing the accuracy of finite differences in computing derivatives and integrals.

Numerical Differentiation and Integration

Covers numerical differentiation and integration techniques using examples and quadrature formulas.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Root Finding Methods: Secant and Newton's Methods

Covers numerical methods for root finding, focusing on the secant and Newton's methods.

Numerical Modelling of the Atmosphere

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

Numerical Integration Methods

Explores numerical integration methods and their application in solving differential equations and simulating physical systems.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Numerical Derivatives: First Order, Backward Finite Difference Formulas

Discusses the error between f'(x0) and its approximation using a backward finite difference formula.

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

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

Finite Difference Methods: Stability Analysis

Explores the stability analysis of finite difference methods for solving differential equations.

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Numerical Methods in Biomechanics: Hip-A

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

Fixed Point Theorem: Convergence of Newton's Method

Covers the fixed point theorem and the convergence of Newton's method, emphasizing the importance of function choice and derivative behavior for successful iteration.