20410619 - ME430 - FOUNDATIONS AND HISTORY OF MATHEMATICAL ANALYSIS

Revisiting the fundamental structures and concepts of mathematical analysis from a historical and critical point of view, also in light of the specific learning objectives of upper secondary school. Knowing how to design learning units on central themes for mathematical analysis in the context of a school course.

scheda docente | materiale didattico

Programma

History of infinitesimal calculus. The Greeks and the calculation of areas and volumes. Cavalieri's indivisibles. Descartes, Fermat.
The birth of calculus: Newton and Leibniz. The development of calculus: the Bernoullis, de l'Hôpital, Euler, and Lagrange.
The father of mathematical analysis: Cauchy. Weierstrass. The Riemann integral. The axiomatization of the real numbers: Cantor and Dedekind.
The Lebesgue integral. The qualitative study of differential equations: Poincaré. Functional analysis: Hilbert, Banach, and von Neumann.

Testi Adottati

E. Giusti, Analisi Matematica 1
E. Giusti Piccola storia del calcolo infinitesimale dall'antichità al Novecento

Modalità Erogazione

5 hours of frontal teaching a week live remote lesson and recording of the lesson itself.

Modalità Frequenza

not compulsory

Modalità Valutazione

written test with exercise and subsequent oral test