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Course# MATH-251(b): Numerical analysis

Summary

L'étudiant apprendra à résoudre numériquement divers problèmes mathématiques. Les propriétés théoriques de ces méthodes seront discutées.

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Related courses (72)

Lectures in this course (13)

Related concepts (211)

Related MOOCs (41)

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail.

Construction and analysis of numerical methods for the solution of problems from linear algebra, integration, approximation, and differentiation.

Machine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practi

This course aims to introduce the basic principles of machine learning in the context of the digital humanities. We will cover both supervised and unsupervised learning techniques, and study and imple

Data

In common usage and statistics, data (USˈdætə; UKˈdeɪtə) is a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures.

Matrix decomposition

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.

LU decomposition

In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix.

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Big data

Big data primarily refers to data sets that are too large or complex to be dealt with by traditional data-processing application software. Data with many entries (rows) offer greater statistical power, while data with higher complexity (more attributes or columns) may lead to a higher false discovery rate. Though used sometimes loosely partly because of a lack of formal definition, the interpretation that seems to best describe big data is the one associated with a large body of information that we could not comprehend when used only in smaller amounts.

Linear Systems: Chapters 4, 5, 6

Explores the link between linear systems and optimization through elimination and LU decomposition.

Transport Equations: Convection and Diffusion

Explores transport equations, emphasizing conservation principles and scheme stability.

Waves and Diffusion: Fundamentals

Covers the fundamentals of waves, diffusion, and convection, focusing on the concepts of propagation, initial conditions, and boundary conditions.

Differential Equations: Approximation Methods and Analysis

Covers methods for approximating solutions to differential equations and their real-world applications.

Finite Elements: Problem with Limits

Covers the application of finite element methods to solve boundary value problems in one dimension.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 2)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.