Lectures related to Finite Differences Formulas: Error Analysis

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.

Numerical Differentiation and Integration

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

Numerical Differentiation: Part 1

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

Numerical Differentiation: Backward and Central Differences

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

Numerical Differentiation: Finite Differences

Explores numerical differentiation using finite differences and addresses the impact of errors in computer computations.

Numerical Methods: Differential Equations and Stability Analysis

Covers numerical methods for solving differential equations and their stability analysis, focusing on error calculation and practical applications in engineering and science.

Finite Differences and Finite Elements: Variational Formulation

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Finite Difference Grids

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

Numerical Analysis: Polynomial Interpolation Techniques

Provides an overview of polynomial interpolation techniques in numerical analysis, focusing on Lagrange interpolation and error estimation methods.

System of ODEs

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

Consistency and Stability in Numerical Methods

Explores consistency and stability in numerical methods, emphasizing error analysis and the role of boundary conditions.

Numerical Differentiation and Integration

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

Numerical Methods: Boundary Value Problems

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

Numerical Methods: Order of Accuracy

Covers the concept of order of accuracy in numerical methods and its implications on final results.

Polynomial Approximation: Stability and Error Analysis

Explores challenges in polynomial approximation, stability issues, and error analysis in numerical differentiation.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Verification and validation

Covers the verification and validation process in numerical flow simulation, ensuring credibility of simulation outcomes.

Numerical Derivatives: Finite Central Differences (2)

Explores the accuracy of central finite difference formulas for derivatives.

Numerical Methods: Euler Schemes

Focuses on Euler schemes for numerical approximation of forces and velocities.

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.