Analyse II

Formal logic: propositions, predicates, tautologies, techniques of proofs. Series of real and complex numbers, sequences and series of functions; pointwise convergence, absolute convergence, uniform convergence, convergence in supremum norm and convergence in the mean-square sense. Power series, Fourier series. Generalized integrals and derivation of functions defined by integrals. Linear differential equations: initial value problems, boundary value problems, Sturm-Liouville problems, Green's function. Second order linear partial differential equations: characteristic curves and Cauchy-Kovaleska problem, well-posed problems, wave equation, heat equation, Laplace and Poisson equations. Surface Integrals, divergence, rotational, Theorems of Green, Stokes and Ostrogradski.

Study the basic concepts and tools of real analysis necessary for the engineering sciences in general, as well as developing the ability to go further in mathematics when needed.

Cours co-requis

Courses requiring this course

Cours ayant celui-ci comme co-requis

Lectures and supervised exercises.

Contribution to the teaching profile

Solve complex scientific problems

References, bibliography, and recommended reading

• T. Tao: Analysis II, Hindustan Book Agency, India, 2006.
• W.E. Boyce and R.C. Di Prima: Elementary differential equations and boundary value problems, Wiley, New York, 1991.
• G.F. Simmons: Differential equations with applications and historical notes, McGraw-Hill, 2017.
• W.A. Strauss: Partial differential equations, Wiley, New York, 1992.

Course notes

• Syllabus
• Université virtuelle

Contacts

Prof. (Analyse 2A): Thomas Lessinnes : Thomas.Lessinnes@ulb.be
Prof. (Analyse 2B): Jérémie Roland: Jeremie.Roland@ulb.be

Campus

Solbosch

Method(s) of evaluation

• written examination

written examination

A written examination in January (Analyse 2A) and another written examination in May or June (Analyse 2B), both on both theory and exercises. Open questions are asked where the ability of applying the notions and theorems in a slightly different framework is tested, together with the ability to elaborate and write down careful proofs.
Two second session written examinations in August following the same modalities as in first session (one written exam for each part, with possible exemption of one of the exams in case of a grade higher or equal to 10/20 for the corresponding part).

Mark calculation method (including weighting of intermediary marks)

The arithmetic mean of the grades for the examinations of Analyse 2A and Analyse 2B, rounded to the nearest half-integer.
If the credits of the course are not acquired after a given evaluation session, any partial grade (Analyse 2A or Analyse 2B) that is higher or equal to 10/20 will be automatically transferred to the next session. In no circumstances will a grade strictly lower than 10/20 be transferred to another session.

Language(s) of evaluation

• french