## MATHEMATICS

-knowledge of the basic tools of logic and mathematics, including:

-elementary algebra, powers, absolute value, equations and inequalities;

-algebraic expressions;

-basic shapes in geometry and their properties;

-basic principles in analytical geometry;

-formulate in mathematical terms, a situation or problem;

-to determine whether a statement is true or false, in a situation and under certain conditions.

-written and oral exam, with exercises and some theoretical questions, 2 hours of time for the practise part.

-during the first semester there will be some exercises, which will allow to pass the first part of the exam.

- model a problem and translate it into mathematical language,

-understand the mathematical concept of sets and know how to use in practice,

-understand the concept of real number,

use the Cartesian coordinate system and be able to translate the algebraic information into graphics information,

-understand the concept of limit of a function and its applications to the study of the graph of a function,

-understand the concept of a function and use in models,

-understand the concept of derivative of a function and its applications to the study of the function's graph,

-state theorems, and understand the proof

Elements of set theory.

Common number sets and their properties. Completness of Real number. Elements of complex numbers.

Mathematical induction.

Cartesian coordinate system, lines in the plane and distances.

The circle in the plane.

Functions. Elementary functions and their graphs.

Limit of a function. Main theorems on limits.

Function composition and inverse functions.

Continuous and discontinuous functions. Main theorems on continuous functions.

Derivative of a function and tangent line.

Basic derivative rules. Maxima and minima of a function.

Main theorems on derivatives.

Graph of a function.

Higher derivatives.

We recommend the following text:

-R.A. Adams, C. Essex, Calcolo Differenziale 1, casa editrice ambrosiana

-face to face,

-practise exercises

The teacher receive students once a week. The day has to be planned by a phone call or via email.

Contacts:

fgladiali@uniss.it

079-228623

The topics of the exam are contained in the text, chapters P,1,2,3,4