italian version

Aims :

The aim 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. Modulus and powers. Exponential, logaritmic and angular functions. Limit of real sequences and its properties. Indeterminate forms. Monotone sequences. The Neper's number and related limits. Asymptotic comparison. Series. The Geometric and Harmonic Series. Convergence tests. Absolute convergence. Leibnitz Theorem. 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 :

Friday 14-16