Descriptif
Series of functions, differential equations (FMA_2S007_EP) builds upon the topology notions studied in Topology and multivariable calculus (FMA_2F002_EP) to allow for a more profound study of functions. Examining functions as limits of simpler ones (e.g. for approximation problems) is made possible in a rigorous manner thanks to topological ideas. This provides the possibility of using crucial tools in many scientific fields; the most striking one being Fourier series (first designed to solve the heat equation and now ubiquitous in science and, in a hidden manner, in daily life). The second part of the course deals with a wide array of differential equations, permitting students to better understand complex physical questions.
Objectifs pédagogiques
At the end of this course, students should feel comfortable with the vairous notions of convergence of sequences and series of functions, especially power series and Fourier series. They will also know the basics of the analysis of ordinary differential equations.
Diplôme(s) concerné(s)
Parcours de rattachement
Pour les étudiants du diplôme Programmes d'échange internationaux
Vous devez avoir validé l'équation suivante : UE FMA_2F002_EP
One variable and multivariable calculus (differentiation, integration, numerical series), fundamentals of topology of normed vector spaces as seen in any first or second year undergraduate class (such as FMA_2F002-EP).
Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Vous devez avoir validé l'équation suivante : UE FMA_2F002_EP
One variable and multivariable calculus (differentiation, integration, numerical series), fundamentals of topology of normed vector spaces as seen in any first or second year undergraduate class (such as FMA_2F002-EP).
Format des notes
Numérique sur 20Littérale/grade américainPour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Vos modalités d'acquisition :
- le rattrapage est obligatoire si :
- Note initiale < 10
- le rattrapage peut être demandé par l'étudiant si :
- Note initiale < 10
- Crédits ECTS acquis : 5 ECTS
La note obtenue rentre dans le calcul de votre GPA.
Pour les étudiants du diplôme Programmes d'échange internationaux
Vos modalités d'acquisition :
- le rattrapage est obligatoire si :
- Note initiale < 10
- le rattrapage peut être demandé par l'étudiant si :
- Note initiale < 10
- Crédits ECTS acquis : 5 ECTS
La note obtenue rentre dans le calcul de votre GPA.
Programme détaillé
I. Pointwise vs. uniform convergence of sequences and series of functions
II. Power series
III. Fourier series
IV. Ordinary differential equations