Lectures in course MATH-250: Advanced numerical analysis I

Numerical Analysis: Nonlinear Equations

Covers algorithms for solving mathematical problems approximately using a computer, including nonlinear equations and numerical approximation methods.

Numerical Analysis: Algorithms and Concepts

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

Bisection Method: Nonlinear Equations

Covers the bisection method for finding zeros of nonlinear functions.

Bisection, Stop Criteria

Explains the bisection method for nonlinear equations and how to determine stop criteria.

Nonlinear Equations: Fixed Point Method

Covers the topic of nonlinear equations and the fixed point method.

Numerical Integration: Quadrature Formulas

Covers numerical integration using quadrature formulas for accurate results.

Numerical Analysis: Quadrature Formulas

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

Bisection Method: Example

Focuses on using the bisection method to approximate function roots with precision.

Nonlinear Equations: Convergence and Taylor Polynomials

Explores nonlinear equations, emphasizing convergence and Taylor polynomials for function approximation.

Polynomials: Legendre and Gauss

Explores Legendre polynomials properties and their use in numerical integration.

Newton Method: Nonlinear Equations

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

Nonlinear Equations: Interpolation and Error Analysis

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

Interpolation of Functions

Covers interpolation of functions, multilayer perceptron, hidden layers, and Lagrange polynomials.

Numerical Integration: Introduction

Introduces numerical integration methods and chemical reaction kinetics principles.

Newton's Method: Graphical Approach

Illustrates the Newton's method graphically, discussing convergence and extreme cases.

Fixed Point Method: Nonlinear Equations

Introduces the fixed point method for solving nonlinear equations by transforming the problem into an equivalent form.

Approximation of Functions

Covers the topic of approximating functions using polynomials through interpolation, emphasizing the importance of optimal point selection.

Numerical Integration: Simpson Quadrature Rule

Covers the Simpson quadrature rule for numerical integration, explaining the method to compute integrals using interpolation nodes and weights.

Linear Systems: Factorization and Cholesky

Explores linear systems, Cholesky factorization, LU factorization, and matrix precision.

Analyzing Analytic Functions

Covers the analysis of analytic functions and the Runge phenomenon in function approximation.