Lectures related to Numerical Derivatives: Finite Difference Formulas

Numerical Differentiation: Part 1

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

Numerical Differentiation

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 Derivatives: Finite Central Differences (2)

Explores the accuracy of central finite difference formulas for derivatives.

Thomas algorithm, accuracy of direct methods

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

Numerical Differentiation: Finite Differences

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

Consistency and Stability in Numerical Methods

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

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.

System of ODEs

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

Numerical Differentiation and Integration

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

Polynomial Approximation: Stability and Error Analysis

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

Numerical Derivatives of Order 1, Rounding Errors

Discusses numerical derivatives of order 1 and the effects of rounding errors on calculations.

Numerical Differentiation and Integration

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

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.

Euler Forward Method

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

Verification and validation

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

Numerical Methods in Matlab

Covers derivation, integration, and simulation in Matlab, along with the representation of numbers and potential errors.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.