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Algebra and analysis


Programme (detailed contents):

Laplace transform. Euclidian spaces, othogonal projection, quadratic forms. Normed vector spaces in finite and infinite dimension. Multivariate calculus : continuity, differentiability, research of extremum. Multiple integrals.






v  Lectures with lecture notes.

v  Exercise sessions.

v  Personal work.



Main difficulties for students:

Acquire the necessary rigour, handle abstracts concepts, perform mathematical demonstrations.



At the end of this module, the student will have understood and be able to explain (main concepts):

Scalar product and orthogonal projection, normed vector spaces, differentiability of multivariate functions, multiple integrals.



The student will be able to:

Solve differential equation with the Laplace transform,

find the extrema of multivariate functions, compute multiple integrals and perform change of variables in it.

Needed prerequisite

First year mathematics

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...


Bilinear algebra, multivariate calculus.

Additional information

First year mathematics.