- 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)
Second cycle degree programme (LM) in Mathematics (cod. 8208)
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
Hausdorff measure.
Integral on parameterized sets.
Integration by parts in multiple integrals.
Divergence theorem.
Exterior differential calculus.
Stokes' theorem.
Applications.
Real trigonometric polynomials.
Fourier polynomials.
Fourier series.
Pointwise and uniform convergence.
Abel convergence.
Poisson integral.
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