Mathématics (06POBMAT)

Coefficient : 2.5
Hourly Volume: 66h (including 36h supervised)
CTD : 36h supervised (and 6h unsupervised)
Out-of-schedule personal work : 24h

Description

AAv1 [heures: 18,B1,B2,B3] (diagonalization) : At the end of this course, students will be able to diagonalize a square matrix and geometrically interpret the characteristic elements (eigenvalues, eigenvectors, eigensubspaces). They will be able to apply this to situations such as solving a system of recurrent sequences, calculating the power of a matrix or solving a linear differential system with constant coefficients.
AAv2 [heures: 15, B2,B3] : At the end of this course, each student will be able to prove the continuity or non-continuity of a function of 2 or 3 variables, calculate partial first and second derivatives, particularly in situations involving the composition of functions and changes of variables.
AAv3 [heures: 18, B2,B3] : At the end of this course, each student will be able to search for and classify critical points (and possible extrema) independently according to the sign of the Hessian determinant. He/she will be able to suggest avenues in the case not determined by the classification.
AAv4 [heures: 15, B2,B3] : At the end of this course, in relation to physics situations such as the study of vibrating strings or the evolution of the temperature of a bar, each student will be able to solve elementary differential equations (linear 1st and 2nd order), to apply or propose a change of variable in order to return to the simple case, and to specify solutions verifying boundary conditions.

One long continuous assessment (coefficient 1) and the average of several short continuous assessments (coefficient 3).

Functions of several variables, partial derivatives, extrema, simple and multiple integrals, curvilinear and surface integrals.

Mathematics S5O content

All analysis books for first and second year preparatory classes.