MATH-251(a): Numerical analysis

Lectures in this course (53)

Explores spline interpolation, least-squares approximation, and error analysis in interpolation.

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

Covers the numerical approach to derivative calculation, focusing on formulas and methods such as fine differences.

Explains the concept of least-squares approximation and its computation in specific and general cases.

Covers the concept of numerical integration using quadrature formulas.

Covers numerical differentiation, integration, finite differences, Taylor expansions, and interpolation polynomials.

Covers digital integration, accuracy, adaptive formulas, sub-intervals, and the midpoint.

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

Explains numerical integration through quadrature formulas and methods like Simpson's formula.

Explains error estimation in numerical integration, focusing on completeness and accuracy.

Introduces Simpson's rule for numerical integration and Richardson extrapolation for accuracy improvement.

Introduces the Gauss elimination algorithm for solving linear systems with practical examples in Python.

Explores linear systems, direct methods, Gauss elimination, LU decomposition, and computational complexity.

Covers the solution of linear systems using direct methods and the evolution of matrices.

Explores the effect of rounding errors in solving linear systems using the LU factorization method.

Explores linear systems, Gaussian elimination, LU decomposition, and matrix types.

Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.

Explores LU factorization, rounding-off errors, sparse matrices, and matrix operations using MATLAB.

Explores linear systems, covering direct and iterative methods for solving them with a focus on round-off errors and Richardson's algorithm.

Explores iterative methods for solving linear systems with a focus on error control.

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