Università Roma Tre

Differentiability, derivatives and their interpretation. Rules of derivation, relation with monotonicity. Fundamental theorem of differential calculus (Fermat, Rolle, Cauchy, Lagrange). The Bernoulli-Hopital theorem. Critical points. Primitive functions and their properties. Some methods for determining primite functions. Second order derivatives, convexity. Qualitative study of functions.
Higher order derivatives and Taylor's formula. Use of Taylors formula for approximations and limits. Riemann integration: partial sums and integrability. Classes of integrable functions (monotone functions, piecewise continuous functions). Generalized integrals, parallel with series.

[G2] Giusti, E.: Analisi Matematica 1, Seconda Edizione Bollati Boringhieri,