Lecture

Analytical Solutions: EDO

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In course

MATH-301: Ordinary differential equations

Ce cours donne une introduction rigoureuse au principaux thèmes de la théorie des équations différentielles ordinaires (EDO). Les EDO sont fondamentales pour l'étude des systèmes dynamiques et des équations aux dérivées partielles. Des applications dans ce ...

Description

This lecture covers the analytical solutions of ordinary differential equations (EDO), focusing on finding solutions for different types of EDOs. The instructor explains the process step by step, from identifying the type of EDO to applying the appropriate analytical methods to solve it. The lecture also delves into the concept of critical points and isolated points in the context of EDO solutions, providing a comprehensive understanding of the topic.

Instructors (2)

François Samer Genoud

2000-2005 Etudes en Physique à l'EPFL dont une année d'échange à Zürich (ETH, 2002-2003). 2005 Diplôme de Physicien EPF (Master) en physique mathématique, sous la direction du Prof. C.-E. Pfister. 2005-2008 Doctorat sous la direction du Prof. C.A. Stuart, sur l'étude de certaines équations de Schrödinger non-linéaires, en particulier de questions liées à l'existence et la stabilité orbitale d'ondes stationnaires. 2009-2010 Chercheur postdoc FNS à OxPDE, Université d'Oxford. 2010-2013 Chercheur postdoc à l'Université Heriot-Watt, Edimbourg. 2013-2014 Chercheur postdoc à l'Université de Vienne. 2015-2017 Professeur Assistant à TU Delft. 2017-2018 Professeur Associé à l'Université libre de Bruxelles. 2018- Directeur du CMS Domaines d'intérêt scientifique: analyse non-linéaire, calcul des variations, équations aux dérivées partielles, physique mathématique et physique théorique en général.

Joachim Krieger

Official source

Related concepts (32)

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).

Analytic philosophy

Analytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, United States, Canada, Australia, New Zealand, and Scandinavia, and continues today. Analytic philosophy is often contrasted with continental philosophy, coined as a catch-all term for other methods, prominent in Europe. Central figures in this historical development of analytic philosophy are Gottlob Frege, Bertrand Russell, G.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

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