- 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:
Second cycle degree programme (LM) in
Mathematics (cod. 5827)
Also valid for First cycle degree programme (L) in Mathematics (cod. 8010)
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from Feb 19, 2025 to Apr 04, 2025
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from Apr 09, 2025 to May 28, 2025
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 and Hausdorff measure.
Integrals on parameterized sets.
The divergence theorem.
Differential forms.
Stokes' theorem.
Applications.
Part 2 - Montanari
Trigonometric and Fourier polynomials.
Expansion in Fourier series.
Bessel's inequality.
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