Lectures related to Numerical Analysis: Introduction to Interpolation Techniques

Computational Science and Engineering: Master Program Overview

Outlines the Master in Computational Science and Engineering program at EPFL, detailing its structure, projects, and career opportunities for graduates.

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.

Numerical Analysis: Polynomial Interpolation Techniques

Provides an overview of polynomial interpolation techniques in numerical analysis, focusing on Lagrange interpolation and error estimation methods.

Numerical Integration: Lagrange Interpolation Methods

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

Error Analysis and Interpolation

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

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.

Polynomial Approximation: Stability and Error Analysis

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

Master in Computational Science and Engineering Overview

Outlines the Master in Computational Science and Engineering at EPFL, detailing its structure, admission criteria, and career opportunities for graduates.

Finite Differences and Finite Elements: Variational Formulation

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Introduction to Computational Science: Course Overview and Objectives

Introduces the Computational Science option at EPFL, detailing course objectives and programming fundamentals using Python.

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.

Lagrange Interpolation: Case 2

Explains Lagrange interpolation with M=2, covering base polynomials and linear independence.

Master's Program in Computational Science and Engineering

Outlines the Master's program in Computational Science and Engineering at EPFL, detailing its structure, curriculum, and career opportunities for graduates.

Numerical Methods: Stopping Criteria, SciPy, and Matplotlib

Discusses numerical methods, focusing on stopping criteria, SciPy for optimization, and data visualization with Matplotlib.

Finite element methods

Covers finite element methods for solving diffusion problems in porous media, including meshing, interpolation, and weighted residuals.

Approximation of Data

Covers the least squares method for approximating data and handling errors.

Isoparametric Formulation of Quad4 Element

Covers the isoparametric formulation of the Quad4 planar element and stiffness matrix calculation.

Root Finding Methods: Bisection and Secant Techniques

Covers root-finding methods, focusing on the bisection and secant techniques, their implementations, and comparisons of their convergence rates.

Introduction to NumPy: Basics of Scientific Computing

Introduces NumPy, focusing on array creation, manipulation, and its advantages for scientific computing.