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MOOC# Numerical Analysis for Engineers

Description

Ce cours contient les 7 premiers chapitres d'un cours donné aux étudiants bachelor de l'EPFL. Il est basé sur le livre "Introduction à l'analyse numérique", J. Rappaz M. Picasso, Ed. PPUR. Il aborde des outils de base et la question de la résolution numérique d'équations différentielles.

Official source

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Instructor

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Lectures in this MOOC (64)

Euler Progressive Scheme

Explains the Euler progressive scheme, its advantages, disadvantages, and stability in approximating values.

Higher Order Schemes

Explores higher-order schemes for solving differential equations and their stability analysis compared to other methods.

Decomposition LLT: Example

Explains the decomposition LL² with an example and detailed calculations.

Numerical Derivatives of Order 1: Finite Difference Centered

Covers numerical derivatives of order 1 using the finite difference centered formula.

Differential Equations: Numerical Methods

Covers the solution of first-order differential equations using numerical methods.

Related concepts (102)

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Free surface

In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere (gas mixture). Unlike liquids, gases cannot form a free surface on their own. Fluidized/liquified solids, including slurries, granular materials, and powders may form a free surface. A liquid in a gravitational field will form a free surface if unconfined from above.

Related publications (245)

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables fas

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this re

Aluminium is a metal sought in the industry because of its various physical properties. It is produced by an electrolysis reduction process in large cells. In these cells, a large electric current goe