29145 - Integrational Elements of Mathematical Analysis L

Learning outcomes

The course will enable the students to learn the basic mathematical tools concerning with Fourier series and Fourier and Laplace transforms (via the knowledge of some basic functional and complex Analysis); applications to ODEs and PDEs will also be considered.

Course contents

Fourier Series:

Main definitions; Fourier series convergence theorems for a periodic function.

Holomorphic function:

The Cauchy Theorem; Laurent series; the Residue Theorem and the calculation of some integrals using the Residue Theorem.

Laplace transform:

Main definitions concerning the Laplace transform; Convergence domain. Calculation rules. Application to Linear ODEs.

Fourier Transform:

Main definitions relating to the Fourier transform of an L^1 function (and references to the L^2 case). If time permits, applications to PDEs.

Readings/Bibliography

G.C. Barozzi, Matematica per l'informazione, Zanichelli

Teaching methods

The course consists of theoretical lessons at the blackboard. If needed, we will move to the blended mode.

Assessment methods

The exam consists ONLY of a written examination (3 hours long) in which the student will be asked to solve a few exercises and to answer to theoretical quetsions.

Note: the student is allowed to to register to a written examination even in case of failure in the previous exam.

Dates: 3 exams in January/February, 1 in June, 1 in July and 1 in September.

Use Almaesami to book for the examination dates and pay attention to register in the proper time.

Teaching tools

Additional material on virtuale.

Office hours

See the website of Eugenio Vecchi