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Complements of Mathematics II

Schedule

Tuesday, 14 January 2020 to Thursday, 28 May 2020
Total hours: 40
Hours of lectures: 20
Hours of supplementary teaching: 20

Examination procedure

  • Written test
  • oral exam

Prerequisites

First year students in Mathematics, Physics and Chemistry

Syllabus

Metric spaces, completeness and the contraction theorem.

Sequences and series of functions, pointwise and uniform convergence.
Power series. Limits of derivatives and integrals.
Functions of several real variables. Partial and directional derivatives. Differential. Total
differential theorem. Hessian matrix.
A few hints on functions from Rn to Rm, Jacobian matrix, differentiation of composite functions.
Implicit functions. Regular curves. Conservative vector fields and potentials.
Differential equations and Cauchy problems. Local existence and uniqueness theorem. Linear differential equations and systems.

 

 

Educational goals:

Goal of the lectures is to introduce students to basic topics but under an advanced and stimulating viewpoint, offering relevant additional elements with respect to traditional courses.


Bibliographical references

Notes.