Università Roma Tre

Numbers (natural, integers, rationals, reals). Functions, their graphs. Injective, monotone, periodic functions. Composition and inversion of functions. Interpretation of the graph of a function. Elementary functions. Sequences and limits. Examples. Operations on limits, sum product and composition. Orders of magnitude. Some notable limits. Continuous functions. Differentiable functions. Geometric interpretation of the derivative. Derivative of elementary functions. Derivative of the product, sum, composition of functions. Second derivatives. Maxima and minima. Rolle and lagrange theorems. Monotone functions. Theorem de l'Hopital. Taylor formula. Primitives and basic properties. Integration by parts and substitution. Rational functions. Definition of integrable function, the fundamental theorem of integral calculus.

Marcellini-Sbordone Elementi di Matematica,
Calculus, Apostol