NUMERICAL SETS
Definition of set and operations between sets. Properties. Cartesian product, equivalence and order relations. Set of natural, integer, rational, real numbers and their properties. Infimum and supremum of a set. Intervals, neighborhoods, open and closed sets.

VECTORS
Definitions and examples of vectors. Operations on vectors. Versor. Scalar product. Cross product of vectors. Examples.

VECTOR SPACE

Space R^n. Definition and basic properties. Subspaces. Linear dependence and independence. Bases and dimensions. Examples. Normed vector spaces and inner product spaces.

INTRODUCTION TO MATRIX CALCULATIONS
Definition of matrix. Sum between matrices, matrix product and their properties. Transposed matrix. Definition of determinant and its properties. Calculation through the Laplace formula. Inverse matrix. Rank of a matrix. Examples.

LINEAR SYSTEM
Linear systems. Examples. Homogeneous systems. Cramer's rule. Rouché-Capelli theorem. Matrix diagonalization. Introduction to eigenvalues and eigenvectors. Algebraic multiplicity and geometric multiplicity.

ELEMENTS OF ANALYTIC GEOMETRY IN THE PLANE AND IN SPACE
Lines, Circumference, ellipse, hyperbola and parabola in the plane. Examples. Equation of straight line in space. Parallelism and orthogonality between straight lines. Plane in space. Parallelism and orthogonality between straight line and plane. Orthogonality between planes. Examples.

ELEMENTARY FUNCTIONS
Definition of function. Injective, surjective, bijective and invertible functions. Monotonic functions. Composition between functions.
Exponentiation with natural and real exponent and its properties. Root extraction and its properties. Exponential function and its properties. Logarithm function and its properties. Trigonometric functions and properties. Inverse trigonometric functions. Function graphs.

LIMITS AND CONTINUITY
Definition, left and right limit. Algebraic operations with limits, indeterminate forms and notable limits.

DIFFERENTIAL CALCULUS FOR FUNCTIONS
Derivative: definition and geometric meaning. Tangent line. Derivatives of elementary functions, rules of derivation, derivative of compound functions; application of derivatives to the calculation of limits: de l'Hopital theorem. Application of derivatives to the study of functions: Fermat's theorem. Maximum and minimum, second derivative, convexity and concavity. Asymptotes. Study of the graph of a function.

INTEGRAL CALCULUS FOR FUNCTIONS
Definition and properties of the definite and indefinite integral, immediate integrals, integration methods by decomposition, by substitution and by parts. Calculation of areas of plane figures.

Analisi Matematica 1 con elementi di geometria e algebra lineare. Bramanti, Pagani, Salsa. Zanichelli (ed. 2014)
Elementi di analisi matematica 1. Versione semplificata per i nuovi corsi di laurea. Marcellini, Sbordone. Liguori (ed. 2002)
Esercitazione di matematica Vol 1. Marcellini, Sbordone. Liguori
Esercitazione di matematica Vol 2. Marcellini, Sbordone. Liguori