Learning outcomes

The aim of the course is to introduce some fundamental topics of infinitesimal, differential and integral calculus of real valued functions in one real variable. Moreover some elements of linear algebra will be introduced.

Program

1) Set theory.
2) The real numbers system. The rational, integer and natural numbers. The induction principle.
3) The Cartesian product of two sets and the relations. Equivalence relations.
4) Polynomials in one indeterminate with coefficients in a field: definition, roots of a polynomia, division algorithm, Ruffini theorem.
5) Functions: definition, injective, surjective, bijective functions, inverse of a function, composition of functions, even and odd functions, monotonic functions. Graph of a function in one real variable. Classification of functions: algebraic and transcendental functions. The graph of a linear and quadratic function. Exponential, logarithmic and goniometric functions.
6) Limits: definition and fundamental theorems.
7) Continuous functions. Dicontinuity of a function.
8) Differentiable functions. Fundamental derivatives and fundamental theorems concerning differentiable functions.
9) Study of a function.
10) Riemann integral. Methods of integration.
11) Linear algebra: matrices and operations, square matrices, determinant of a square matrix, properties of determinants, inverse matrix of a square matrix, linear systems.
12) Sequences and series.

Examination Methods

Written and oral exam.