66698 - Mathematical Analysis Complements

Learning outcomes

At the end of the course, the student knows the basic ideas and techniques of differential and integral calculus on manifolds. He acquires the main knowledge about the trigonometric series and their pointwise, uniform and quadratic mean convergence. He knows how to use the skills acquired in the mathematical models of applied sciences and engineering.

Course contents

Part 1 - Martino
- Outline of measure theory.
- Hausdorff measure.
- Hausdorff integral.
- The divergence theorem.
- Differential forms.
- Stokes' theorem.
- Applications.


Part 2 - Montanari
- Trigonometric polynomials.
- Fourier polynomials.
- Expansion in Fourier series.
- Gibbs phenomenon. Fejér series.
- Poisson kernel.
- Complex Fourier series.
- Applications.

Readings/Bibliography

Ermanno Lanconelli
Lezioni di Analisi Matematica 2, Seconda Parte.
Pitagora Editrice Bologna


Walter Rudin
Principles of Mathematical Analysis, Third Edition.
McGraw-Hill


Tom Apostol
Mathematical Analysis, second Edition.
Addison-Wesley Publishing Company

Teaching methods

Lectures in classroom.

Assessment methods

Final oral exam

---------

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 can be found on Virtuale.

Office hours

See the website of Vittorio Martino

See the website of Annamaria Montanari