Elements of Combinatorics:
Arrangements, permutations and simple combinations, binomial coefficients, definitions and properties.

Matrices and Determinants:
Definitions and properties of matrices, diagonal matrices, transposed, opposite and inverse matrices. Operations on matrices, determinants, Laplace's theorems, Sarrus' rule, general properties of determinants, minor and rank or characteristic of a matrix.

Systems of Linear Equations:
Generalities on systems of linear equations, Rouchè-Capelli theorem, Cramer's theorem, systems of m equations in n unknowns, homogeneous systems.

Real Variable Functions:
Trigonometric functions, compound functions, inverse functions, limits of a function, theorems on limits, the uniqueness of the limit, theorem of the permanence of the sign, theorem of comparison, limit of the sum, of the product, of the quotient, etc. .. of functions, notable limits.

Continuous Functions:
Definitions and first properties, continuity, Neper's number, maxima and minima, inverse function.

Derivatives:
Definition and geometric meaning of the derivative, operations on derivatives and derivation rules, derivation of trigonometric functions, derivation of compound and inverse functions, differentiability and continuity, differential, successive derivatives, relative maxima and minima, asymptotes, concavity and convexity, inflections, graphs of functions.
Theorems of Rolle, Cauchy, Lagrange, De L'Hopital, indeterminate forms.

Transcendent Functions:
Inverse trigonometric functions, logarithm function, exponential function, hyperbolic functions.

Integration:
Indefinite integral, definition and properties, relationship between integrability and derivability, immediate integrals, definite integral.

A. M. Bigatti, L. Robbiano. Matematica di base. Casa Editrice Ambrosiana (Milano).