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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?

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Description

Instructor

Marco Picasso

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Lectures in this MOOC (64)

Nonlinear Systems of Equations MOOC: Numerical Analysis for Engineers

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

Systems of First-Order Differential Equations MOOC: Numerical Analysis for Engineers

Explores systems of first-order differential equations and numerical methods for their analysis.

Numerical Testing MOOC: Numerical Analysis for Engineers

Explains numerical testing methods and integration process with examples.

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 LLT: Example MOOC: Numerical Analysis for Engineers

Explains the decomposition LL² with an example and detailed calculations.

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 algebra

Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.