Università Roma Tre

Notion of derivative, rules of differentiation . Derivatives of elementary functions . Sign of the
derivative and monotonicity . Theorems of Rolle , Lagrange , Cauchy and applications . Higher order derivatives . Convex functions , maxima and minima of C2 functions. Theorems of
de l' Hopital . Taylor's formula . Graphs of functions. Riemann integral , linearity , positivity . Integration of continuous functions . Average theorem . The Fundamental theorem of calculus. Integration by parts , by substitution . Integration of elementary functions
; integration of rational functions . Improper integrals , absolute integration .
Areas of plane figures bounded by graphs . Rectifiability and length of the graph of a
C1 function .

Rudin, W: Principles of Mathematical Analysis, McGraw-Hill, 1976