Università Roma Tre

Differentiability of functions. Rules for computing derivatives. Derivatives and monotonicity. Fundamental theorems on derivatives (Fermat, Rolle, Cauchy, Lagrange). Theorem of Bernoulli-Hopital. Critical points. Second derivative. Convex functions. Qualitative study of functions. Successive derivatives and Taylor's formula. Use of Taylor's formula in computing limits.
Riemann's integral: partial sums, integrability. Integrability of monotone and piecewise continuous functions. Computation of primitives. Fundamental theorem of calculus. Integral remainder in Taylor's formula. Improper integrals; comparison with series. Taylor series.

Luigi Chierchia, Corso di Analisi, prima parte, Una introduzione rigorosa all'analisi matematica su R; Dispense AA 2018-2019, libreria Efesto