MOOC

Numerical Analysis for Engineers

Description

This course is based on the book "Introduction à l'analyse numérique", J. Rappaz M. Picasso, Ed. PPUR. Basic tools are described in the first 5 chapters. The last two chapters deal with the numerical solution of differential equations. More specifically, we will study the following chapters of the book:

Chapter 1: interpolation, how to approximate a function by a polynomial? Chapter 2: how to approximate derivatives with finite difference formulas? Chapter 3: How can integrals be approximated by quadrature formulas? Chapters 4,5,6: how to solve (large) linear systems? Chapter 8: How to solve nonlinear equations and systems of equations? Chapter 9: how to approximate the solution of a differential equation (initial value problem)? Chapter 10: How to approximate the solution of a one-dimensional boundary problem using a finite difference method?

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

Instructor

Marco Picasso

Expertise Computational Science and Engineering Mission I am teaching analysis and numerical analysis for engineers and mathematicians at bachelor and master levels.My research pertains to the numerical simulation of complex physical systems with partial differential equations.Here is some bibliometry: Google Scholar, Research Gate, Orcid, here is my most recent CV. Ongoing research projects: - Numerical simulation of aluminium electrolysis, collaboration with RioTinto LRF lab, Ycoorsystems SA and Jacques

About this result

Lectures in this MOOC (64)

Theorem 1.1: Interpolation and Equidistant Points MOOC: Numerical Analysis for Engineers

Covers the concept of interpolation using equidistant points and Theorem 1.1.

Numerical Derivatives of Order 1: Finite Differences Progressive MOOC: Numerical Analysis for Engineers

Covers numerical derivatives of order 1 using progressive finite difference formulas in numerical analysis.

Decomposition LU: Example MOOC: Numerical Analysis for Engineers

Explains LU decomposition with a detailed example and discusses submatrix regularity.

Nonlinear Systems of Equations MOOC: Numerical Analysis for Engineers

Covers methods to solve nonlinear systems of equations in numerical analysis.

Gaussian Elimination Example MOOC: Numerical Analysis for Engineers

Demonstrates the step-by-step process of solving linear equations using Gaussian elimination.

Related concepts (32)

Linear map

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .

X-ray

X-ray radiation, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3e16Hz to 3e19Hz) and energies in the range 124 keV to 145 eV, respectively. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.

Linear independence

In the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.