B6036 - Laboratorio di matematica - Modulo 2: analisi matematIca

Learning outcomes

During the 10 hours of this module the student will deepen his knowledge of some Mathematical Analysis topics from a higher point of view, which can then be presented in class at school.

Course contents

The theme of the integration of the functions of a variable on an interval [a,b] will be explored in depth according to the following schedule:

1. Historical introduction: brief excursus on the salient moments of the development of the integral calculus from Eudoxus to Lebesgue

2. The Riemann integral: the need to surpass the scholastic definition which involves only continuous integrand functions

3. The Fundamental Theorem of the Integral Calculus on the integral of the derivative: various forms of this theorem depending on Riemann or Lebesgue integration. Notable counterexamples.

4. Mention of the not-absolutely-convergent Perron integral, which extends the standard, generalized Riemann and Lebesgue integrals

5. The last 5 hours will treat the typical misconceptions regarding the concept of infinity

Readings/Bibliography

Material will be made available on the Virtual platform

Teaching methods

The ten hours will be delivered in traditional face-to-face mode.

Assessment methods

Eligibility for the course will be given on the basis of the verification of the minimum percentage of attendance and the delivery of any exercises requested during the course. The evaluation of the learning of the teaching contents is contextual to the final test for the acquisition of the teaching qualification in the competition class of the training path, provided for by Art. 9 of the Prime Ministerial Decree of 4 August 2023.

Teaching tools

Educational material on the Virtual platform

Office hours

See the website of Andrea Bonfiglioli