MATH-251(c): Numerical analysis

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Lectures in this course (106)

Iterative Methods Log in to Mediaspace to watch this video

Explores iterative methods for solving linear systems of equations, including Jacobi and Gauss-Seidel.

Iterative Methods: Linear Systems Log in to Mediaspace to watch this video

Covers iterative methods for solving linear systems and discusses convergence criteria and spectral radius.

Ordinary Differential Equations Log in to Mediaspace to watch this video

Covers the approximation of a system of differential equations using a method based on time intervals.

Finite Differences: Definition and Proof Log in to Mediaspace to watch this video

Covers the definition of the center of a function using finite differences and provides step-by-step proofs.

Construction of an Iterative Method II Log in to Mediaspace to watch this video

Covers the construction of an iterative method for linear systems and introduces relaxation and residual analysis.

Polynomial Interpolation: Error and Definition Log in to Mediaspace to watch this video

Explores polynomial interpolation theory, emphasizing error expression and piecewise definition.

Jacobi Method: Convergence Conditions Log in to Mediaspace to watch this video

Explores the Jacobi method for linear systems, emphasizing convergence conditions and matrix properties.

Jacobi Method: Part I Log in to Mediaspace to watch this video

Introduces the Jacobi method for solving linear systems by iteratively updating the diagonal elements of a matrix.

Ordinary Differential Equations Log in to Mediaspace to watch this video

Covers the extension of ordinary differential equations to n-dimensional space.

Linear Systems: Iterative Methods Log in to Mediaspace to watch this video

Covers iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods.

Bisection Method: Nonlinear Equations

Covers the bisection method for finding zeros of nonlinear functions.

Numerical Analysis: Newton's Method Log in to Mediaspace to watch this video

Explores Newton's method for finding roots of nonlinear equations and its interpretation as a second-order method.

Numerical Analysis: Stability in ODEs Log in to Mediaspace to watch this video

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

Untitled Log in to Mediaspace to watch this video

Numerical Analysis: Nonlinear Equations Log in to Mediaspace to watch this video

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Numerical Integration Log in to Mediaspace to watch this video

Explores numerical integration methods, including the composite quadrature formula and the efficiency of Simpson's rule, aiming to enhance student understanding and reduce stress.

Numerical Analysis: Linear Systems Log in to Mediaspace to watch this video

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

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