In the Analysis-Algebra course:
– Laplace transform and application to the resolution of first and second order linear ODEs.
– bilinear algebra: bilinear forms, symmetric bilinear forms, associated quadratic form, scalar product, orthogonality, Gram-Schmidt orthogonalization procedure, orthogonal of a vector subspace, orthogonal projection, norm associated with a scalar product, convergence, continuity, Weierstrass theorem.
– functions of several variables: continuity, partial derivatives, differentiability, local extremum points, multiple integrals.
In the Probabilities section:
– probability space and conditional probabilities, independence of events
– discrete and continuous random variables (law of probability, expectation, variance, etc.)
– couples of random variables
– limit theorems (law of large numbers, central limit theorem)
