Lectures related to Numerical Analysis: Polynomial Interpolation Techniques

Numerical Integration: Lagrange Interpolation Methods

Covers numerical integration techniques, focusing on Lagrange interpolation and various quadrature methods for approximating integrals.

Polynomial Approximation: Stability and Error Analysis

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

Numerical Differentiation: Finite Differences

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

Nonlinear Equations: Interpolation and Error Analysis

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

Numerical Analysis: Introduction to Interpolation Techniques

Covers the basics of numerical analysis, focusing on interpolation methods and their applications in engineering.

Numerical Analysis: Advanced Topics

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.

Lagrange Interpolation

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Numerical integration: continued

Covers numerical integration methods, focusing on trapezoidal rules, degree of exactness, and error analysis.

Piecewise Linear Interpolation

Covers the concept of piecewise linear interpolation and the importance of dividing intervals correctly.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Numerical Differentiation: Methods and Errors

Explores numerical differentiation methods and round-off errors in computer computations.

Interpolation by Intervals: Lagrange Interpolation

Covers Lagrange interpolation using intervals to find accurate polynomial approximations.

Numerical Integration: Lagrange Interpolation, Simpson Rules

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Trigonometric Interpolation: Approximation of Periodic Functions and Signals

Explores trigonometric interpolation for approximating periodic functions and signals using equally spaced nodes.

Numerical Differentiation and Integration

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

Lagrange Interpolation: Numerical Integration Techniques

Covers Lagrange interpolation and its application in numerical integration techniques, focusing on both non-composite and composite methods of quadrature.

Numerical Analysis: Introduction to Computational Methods

Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

Lagrange Interpolation: Polynomial Construction and Definite Integral Introduction

Explores Lagrange interpolation for polynomial construction and introduces the definite integral.

Numerical Integration: Basics

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