Academic Year 2022/2023
- Docente: Vittorio Martino
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- 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)
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from Feb 22, 2023 to May 24, 2023
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
Integrals on parameterized sets.
Outline of measure theory and Hausdorff measure.
The divergence theorem.
Differential forms.
Stokes' theorem.
Applications.
Trigonometric and Fourier polynomials.
Expansion in Fourier series.
Bessel's inequality.
Poisson kernel.
Complex Fourier series.
Applications.
Readings/Bibliography
Walter Rudin
Principles of Mathematical Analysis, Third Edition
McGraw-Hill
Teaching methods
Lectures in classroom.
Assessment methods
Final oral exam
Teaching tools
Additional material can be found on Virtuale
Links to further information
http://www.dm.unibo.it/~martino/
Office hours
See the website of Vittorio Martino