Università Roma Tre

Limits. Continuous functions. Derivability and monotonicity. Second derivative and convexity. Elementary analytic functions (exponential, trigonometric functions and their inverses)
Integrals and areas

Chierchia, L.: Corso di analisi, prima parte. Una introduzione rigorosa all'analisi matematica su R; McGraw-Hill, 2019, 390 pagine

The following key topics will be revisited in depth and introduced from a historical point of view:
1. R and its fundamental subsets
2. Concept of limit and notable limits
3. Series
4. Continuous functions
5. Derivability and monotonicity
6. Second derivative and convexity
7. Elementary analytic functions (exponential, trigonometric functions and their inverses)
8. Integrals and areas
9. The Fundamental Theorem of Calculus
10. Complex numbers

Other course objectives
Analysis of fundamental school evaluation moments such as the tests/problems/questionnaires of the State Exam and the Invalsi tests.
Discussion of ministerial guidelines.

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