Lectures related to Numerical Analysis: Introduction to Computational Methods

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Numerical Analysis: Jupyter Notebook Tutorial

Covers course organization, Jupyter Notebook for Python experimentation, algorithms, interpolation, solving equations, linear systems, and practical applications.

Numerical Analysis: Interpolation and Approximation

Covers linear systems, non-linear equations, and interpolation for numerical analysis.

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 Analysis: Advanced Topics

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

Numerical Analysis: Introduction to Interpolation Techniques

Covers the basics of numerical analysis, focusing on interpolation methods and their applications in engineering.

Finite Element Modeling: Dynamics

Introduces the basics of finite element modeling for dynamics and discusses the Newmark method for time integration.

Numerical Integration: Euler Method

Covers the progressive Euler method for numerical integration of ODEs, including Cauchy problems and Runge-Kutta methods.

Linear Differential Equations: Constant Coefficients and Solution Methods

Covers linear differential equations with constant coefficients and introduces the method of good choice for finding particular solutions.

Runge-Kutta Methods: Approximating Differential Equations

Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.

Finite element methods

Covers finite element methods for solving diffusion problems in porous media, including meshing, interpolation, and weighted residuals.

Introduction to Ordinary Differential Equations

Introduces ordinary differential equations, their order, numerical solutions, and practical applications in various scientific fields.

Finite Differences and Finite Elements: Variational Formulation

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

Power Systems Dynamics: Transient Stability

Explores transient stability in power systems dynamics, covering algebraic equations, generator models, and numerical integration techniques.

Nonlinear Equations: Methods and Applications

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

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 Integration: Lagrange Interpolation Methods

Covers numerical integration techniques, focusing on Lagrange interpolation and various quadrature methods for approximating integrals.

Polynomial Approximation: Stability and Error Analysis

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

Numerical Methods: Euler and Crank-Nicolson

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

Newton's Method: Convergence and Criteria

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.