Lectures related to Numerical Derivatives: Finite Central Differences (2)

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

Discusses numerical differentiation, error analysis, and finite difference formulas.

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 Derivatives: Finite Difference Formulas

Analyzes the error in numerical derivatives using finite difference formulas.

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 Grids

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

Numerical Analysis: Advanced Topics

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

Finite Differences Formulas: Error Analysis

Explores finite differences formulas, error analysis, and numerical experiments in computational mathematics.

Thomas algorithm, accuracy of direct methods

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

Consistency and Stability in Numerical Methods

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

Numerical Methods: Boundary Value Problems

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

Numerical Derivatives of Order 1

Covers the concept of numerical derivatives of order 1 and the importance of choosing a small fixed value for h.

Finite Elements: Problem with Limits

Covers the application of finite element methods to solve boundary value problems in one dimension.

Finite Difference Method: Approximating Derivatives and Equations

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

Numerical Methods: Euler Schemes

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

Numerical Methods for Boundary Value Problems

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

Polynomial Approximation: Stability and Error Analysis

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

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.