italian version

Aims :

The scope of the course is to introduce the students to the basic elements of the Differential and
Integral Calculus

Topics :

Sets, Relations and Functions. Natural, Integer, Rational and Real numbers. The
Induction principle. Limit of real sequences and its properties. Indeterminate forms. Monotone
sequences. The Neper's number and related limits. Asymptotic comparison. Limits of real function
of real variale. Properties. Indeterminate forms. Asymptotic comparison. Monotone functions.
Continuity; The Weierstrass's and the Intermediate Values Theorems. Derivative and Derivative
Formulas. Successive Derivative. The Fermat's, Rolle's, Lagrange's and Cauchy's Theorems.
Derivative and monotonicity. Convexity. Primitives. The De L'Hospital's Theorems. Taylor
Formulas. Asymptots and the study of the graphs of functions. Definite Integral and its properties.
Fundamental Theorem and Formula of the Integral Calculus. Indefinite Integral and integration
methods: sum decomposition, by parts and sostitution. Improper integral and convergence tests.


Textbooks :

P. Marcellini, C. Sbordone, Elementi di Analisi Matematica I,
Liguori Editore

Exam :

Written and oral examination

Tutorial Session :

Thursday 11.30-13.30