MATH-250: Advanced numerical analysis I

Lectures in this course (108)

Introduces the Newton method for solving nonlinear equations through iterative processes and practical examples.

Covers the interpolation of nonlinear functions using Lagrange polynomials and error analysis.

Covers the construction of an iterative method for linear systems by decomposing a matrix A into P, T, and P_A.

Explores the composite quadrature formula, digital integration, and numerical integration techniques using interpolating polynomials.

Covers the concept of numerical derivative and the progressive difference approach for computing derivatives.

Explains the definition and calculation of finite difference centers with proofs and examples.

Covers algorithms for mathematical problems, focusing on stability, precision, and critical result analysis.

Covers numerical integration using quadrature formulas for accurate results.

Covers the Richardson method for solving linear systems and convergence criteria.

Covers optimization techniques related to gradient descent for finding the optimal solution iteratively.

Covers the principles of regression and linear systems, focusing on iterative methods.

Covers the principles and applications of linear regression, focusing on building a simple model to make suggestions.

Introduces QR factorization for matrix decomposition, emphasizing its importance in various applications and the implications of a well-chosen model.

Covers the Fourier transform, compression techniques, and spectral analysis of periodic signals.

Explores data compression fundamentals, techniques, and information preservation.

Covers the concept of Fourier series and their practical applications in signal processing.

Explores the Discrete Fourier Transform, Fast Fourier Transform, orthogonal functions, and trigonometric approximations.

Discusses periodic functions, integrals, and approximations using trigonometric polynomials and proofs of related theorems.

Explores the theory and application of quadrature formulas for numerical analysis.

Explores Legendre polynomials properties and their use in numerical integration.

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