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Cours scientifique - MAA105 : Integral and Differential Calculus

Domaine > Mathématiques appliquées, Mathématiques.

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Descriptif

Integrals and differential calculus (MAA105) develops students's skills in crucial analytical tools, in particular integration. The approach to integration employed in this course is Riemann's integral, a foundational mathematics theory. This course also introduces students to two important and related topics
covered in the Bachelor program: Taylor expansions (a tool for function approximation) and differential equations, which are required to understand basic physical problems (trajectories, populations, etc.).

Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Vous devez avoir validé l'équation suivante : UE MAA102

Format des notes

Numérique sur 20

Littérale/grade américain

Pour les étudiants du diplôme Bachelor of Science de l'Ecole polytechnique

Vos modalités d'acquisition :

Test, homework, mid-term exam, final exam.

Le rattrapage est autorisé

    La note obtenue rentre dans le calcul de votre GPA.

    Programme détaillé

     Integration of functions of one real variable, Riemann sums, fundamental theorem of analysis
     Integration by parts, changes of variables, calculus of primitive functions
     Decomposition of rational fractions
     Taylor formula with integral remainder ; Taylor-Young formula, Landau notations o and O, computations and applications.
     Improper integrals (simple cases), comparison series/integrals
     ODEs

    Mots clés

    Riemann integration; Taylor expansion; differential equations
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