Analysis (04_XBANA)

Coefficient : 2
Hourly Volume: 50h (including 27h supervised)
CTD : 27h supervised (and 4.5h unsupervised)
Out-of-schedule personal work : 18.5h

Description

Generalized integrals: notion of convergence, calculation techniques (integration by parts, change of variable)
Multiple integrals: double and triple integrals - Fubini formulas - Variable changes (polar coordinates for double integrals, cylindrical and spherical coordinates for triple integrals) - Applications to area and volume calculations, determination of a center of inertia, a moment of inertia
Curvilinear integrals - Calculation of lengths of arcs of curves - Circulation of a vector field - Concept of gradient and rotational - Green-Riemann formula, application to area calculations
Surface integrals - Flow of a vector field - Green-Ostrogradsky formula - Stockes-Ampère formula

AAv1 [heures: 25, B1,B2,B3] (multiple integrals): At the end of this course, each student knows how to calculate double and triple integrals, and use these notions to determine volumes, surface areas, coordinates of a center of inertia or the inertia matrix of a solid.
AAv2 [heures: 10, B2,B3] (generalized integrals): At the end of this course, each student knows how to determine the nature (convergent or divergent) of a generalized integral and calculate the value of a convergent integral in different fields (probability, electromagnetism, signal theory, etc.).
AAv3 [heures: 15, B1,B2,B3] (vector_fields): At the end of this course, each student knows how to determine the circulation of a vector field (resp. the curvilinear integral of a differential form) and apply this notion in different situations (electric field, magnetic field, speed of a fluid at a point, etc.).

One long test (coefficient 1), average of several short tests (coefficient 2)

Simple, multiple, curvilinear and surface integrals

Mathematics program for high school and previous semesters