English

Français

English

Français

Appearance

Analysis (04_XBANA) ​

  • Coefficient : 2
  • Hourly Volume: 45h (including 27h supervised)
    CTD : 27h supervised
    Out-of-schedule personal work : 18h

AATs Lists

Description ​

  1. Multiple integrals: double and triple integrals
  • Fubini formulas
  • Change of variables (polar coordinates for double integrals, cylindrical and spherical coordinates for triple integrals)
  • Applications: volume calculations, determination of center of inertia, moment of inertia, surface area.
  1. Generalized integrals: notion of convergence, calculation techniques (integration by parts, change of variable).
  2. Curvilinear integrals
  • Calculation of curve arc lengths
  • Circulation of a vector field
  • Green-Riemann formula, application to area calculations
  1. Probabilities
  • Distribution function of a pair of continuous random variables
  • joint law and marginal laws for continuous random variables

Learning Outcomes AAv (AAv) ​

  • AAv1 [heures: 20, B1,B2,B3] (multiple integrals): At the end of this course, each student will be able to calculate double and triple integrals, and use these concepts to determine volumes, surface areas, the coordinates of a center of inertia or the inertia matrix of a solid.

  • AAv2 [heures: 8, B2,B3] (generalized integrals): At the end of this course, students will be able to determine the nature (convergent or divergent) of a generalized integral and calculate the value of a convergent integral in various fields (probability, electromagnetism, signal theory, etc.).

  • AAv3 [heures: 8, B1,B2,B3 ] (Probabilities) : At the end of this course, students will be able to calculate probabilities for pairs of continuous (joint law, marginal laws) or discrete random variables.

  • AAv4 [heures: 9, 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.).

Assessment methods ​

AAV will be validated by:

  • a long continuous assessment test
  • the average of several short continuous assessment tests

Key Words ​

Simple, multiple, curvilinear and surface integrals. Probability of a set of random variables.

Prerequisites ​

Mathematics program for high school and previous semesters

Resources ​