Course

MATH-251(c): Numerical analysis

Lectures in this course (30)

Covers the definition and proof of fixed point methods, emphasizing the importance of continuity.

Explores the numerical stability of Euler schemes for solving differential equations.

Explores the proof of quadrature, accuracy, exactitude, and interpolation in mathematical calculations.

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

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

Discusses the analysis of composite numerical integration formulas and their convergence, stability, and error characteristics.

Covers the numerical stability analysis of iterative methods and discusses their impact on solution accuracy.

Covers the application of Taylor series in writing functions and solving exercises.

Covers the bisection method for finding zeros of continuous functions.

Covers digital integration, interpolation polynomials, and integration formulas with error analysis.

Explores numerical integration through composite formulas, accuracy estimation, and error evaluation in integration methods.

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

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Covers the construction of an iterative method for linear systems, emphasizing matrix decomposition and convexity.

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

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

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

Explains the spectral radius of a matrix and its generic definition.

Covers the Gauss-Seidel method for solving linear systems through progressive substitution and iterative processes.

Discusses convergence criteria and when iteration stops, focusing on known cases and metrics attention.