- Docente: Vittorio Martino
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Moduli: Vittorio Martino (Modulo 1) Annamaria Montanari (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Mathematics (cod. 8010)
Also valid for Second cycle degree programme (LM) in Mathematics (cod. 5827)
Second cycle degree programme (LM) in Mathematics (cod. 6730)
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
Teaching tools
Additional material can be found on Virtuale.
Office hours
See the website of Vittorio Martino
See the website of Annamaria Montanari