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Analysis (02_XBANA) ​

  • Coefficient : 2
  • Hourly Volume: 52h (including 27h supervised)
    CTD : 27h supervised
    Out-of-schedule personal work : 25h

AATs Lists

Description ​

  • Learning basic integral calculus methods as well as solving elementary differential equations.

  • Integral calculation:

    • Change of variable.
    • Search for primitives in particular cases: Rational fractions, trigonometric polynomials, trigonometric rational fractions.

  • Classical differential equations:

    • 1st order and 2nd order linear with constant coefficients.
    • Examples of nonlinear: with separable variables, Bernoulli.

  • Continuous probability

    • Density of a continuous random variable, distribution function, expectation, variance, quantile.
    • Continuous uniform law, exponential law, reduced centered normal law (Gaussian law).
    • Law of a sum of continuous variables (exponential, uniform, Gaussian).
    • Central limit theorem, approximation of the binomial law by the normal law.

Learning Outcomes AAv (AAv) ​

  • AAv1 [heures: 18, B2, B3] : At the end of this course, each student knows how to implement integral calculation techniques in different situations (calculation of areas, volumes, arc lengths curve) and different fields or disciplines related to engineering (in mechanics, electronics, physics, probability).

  • AAv2 [heures: 18, B1, B2, B3] (differential equations): At the end of this course, each student knows how to solve a physical problem modeled by first and second order differential equations.

  • AAv3 [heures: 8, B1, B2, B3] (probability): At the end of this course, each student is able to model and solve an elementary continuous probability problem.

Assessment methods ​

The AAVs will be validated by:

  • a long Assessment
  • average of several short Assessments

Key Words ​

Integration, differential equations, continuous probabilities.

Prerequisites ​

The content of mathematics S1 and high school specialty mathematics first and final

Resources ​

  • Les mathématiques en licence : cours et exercices résolus. Tome 2 / Azoulay, Avignant, Auliac
  • Introduction à l'analyse : cours & exercices corrigés. Licence 1 mathématiques / Aebischer
  • Mathématiques : 170 fiches-méthodes, 560 exercices corrigés, formulaire / EL Kaabouchi
  • Site Bibm@th (cours, exercices, quizz) https://www.bibmath.net
  • Site Exo7 http://exo7.emath.fr/