Università Roma Tre

- The real field R and its subsets N, Z and Q. Intervals: upper a and lower bounds.
- Inf and Sup, min and max. Theorem of completeness of R. The absolute value of a real number.
- Real function in one real variable. Image and pre-image. Lecture of a graph.
- Composition, translation and absolute value. Injective, surjective, bijective, inverse functions. Symmetries.
- monotonicity, injectivity and related theorems. Lower and upper bounds of functions, local and global extrema.
- basic functions and their inverse (power, exp, logarithm, trigonometric)
- R^2 as a vector space. The scalar product and euclidean plane
- sequences in R: theorems of uniqueness of limit, sign permanence, limit of monotonic sequences, Bolzano-Weierstrass theorem
- equivalence of sequences and properties
- proof of sin(a_n)/a_n —1 when a_n–0.
- o and O
- limit of a functions and related theorems
- continuous functions, theroem of existence of seros, Darboux, sign permanence
- derivative of a function and geometric interpretation. Derivation rules
- characterization of monotonic and convex functions through their derivatives
- primitives and integration
- Riemann integral: construction and example of integrable functions. The fundamental theorem of calculus
- bascs of ODE

Recommended Texts (in italian)

- Elementi di Matematica, Marcellini-Sbordone, Luguori ed. (ATTENZIONE: questo testo non copre tutto il programma)
– Elementi di Calcolo, Marcellini-Sbordone, Luguori ed. (più completo)

Ontherwise any book of Basic Calculus will be fine.

Notes of the project Matematica Assistita - Ariel (Univeristà degli Studi di Milano) download at URL : matematicaassistita.ariel.ctu.unimi.it/ : register as Utente Esterno -- Contenuti -- scegliere l'Argomento