Numerical Analysis: Introduction to Computational Methods

Related lectures (27)

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

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

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

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

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

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

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

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

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

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