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.).
Diplôme(s) concerné(s)
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 20Littérale/grade américainPour 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 autoriséLa 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