04310 - Complementary Fundamentals of Mathematical Analysis

Academic Year 2024/2025

  • Moduli: Vittorio Martino (Modulo 1) Annamaria Montanari (Modulo 2)
  • Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)

    Also valid for First cycle degree programme (L) in Mathematics (cod. 8010)

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