Descriptif
Introduction to analysis (MAA102) is an introductory-level mathematical analysis course that
provides a well-balanced approach between calculus and foun- dational notions ; it is designed to equip
students with the fundamental analytical tools required in all scienti c elds. In particular, this course
covers sequences, series and function study. It also introduces students to important mathematical concepts
which will be expanded upon later in the program : namely, limits, continuity and derivative.
Diplôme(s) concerné(s)
Format des notes
Numérique sur 20Littérale/grade américainPour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique
Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)- Crédits ECTS acquis : 5 ECTS
La note obtenue rentre dans le calcul de votre GPA.
Pour les étudiants du diplôme Echanges PEI
Le rattrapage est autorisé (Note de rattrapage conservée écrêtée à une note seuil de 10)- Crédits ECTS acquis : 5 ECTS
La note obtenue rentre dans le calcul de votre GPA.
Programme détaillé
Real numbers, sup and inf.
Real and complex sequences : limits, comparison methods, in nite limits, subsequences.
Real-valued functions of a real variable : limits, monotonic functions, continuous functions, global
properties of continuous functions. Derivatives of functions.
Variations of functions, convex functions, usual functions.
Taylor-Lagrange theorem and applications.
Real and complex-valued series : convergent and divergent series, series of non-negative numbers,
convergence of real and complex-valued series.