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 (outcome).

Laplace transform:

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

The method of characteristics for first order PDE's.

Readings/Bibliography

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

Teaching methods

The course consists of theoretical lessons at the blackboard.

Assessment methods

The exam consists ONLY of a written examination (3 hours) in which the student will be asked to solve some exercises of the following 3 types:

1. statement and proof of a theorem

2. statement of a theorem

3. three exercises (Laplace transform, Fourier series, methods of the charateristics).

Note: the student is allowed 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.

 

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

Teaching tools

Additional material on the website Virtuale.

Office hours

See the website of Andrea Bonfiglioli