Catalogo dei Corsi di studio

Obiettivi formativi (Inglese): Aim of this module is the achievement, by the students, of the basic means of Mathematical Analysis related to the study of functions of one real variable and their use for the solution of problems in Applied Mathematics, and in particular of Physical and Engineering problems. Special emphasis is devoted to qualitative study and approximate solution of these problems, by virtue of asymptotical techniques, Taylor polynomials etc.
Risultati di apprendimento attesi (Inglese): Successful students will be able to study the behavior of numerical sequences and series; to sketch the complete graph of a function of one variable; to develop the Taylor (or MacLaurin) polynomials of functions of one variable; to study the asymptotical behavior of a function when the independent variable approaches infinity or singularities or zeros; to solve optimization problems in one variable, on bounded and unbounded intervals; to solve definite, indefinite and improper integrals; to solve some kinds of ordinary differential equations, characterizing several Physics and Engineering problems.

Programme

Set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, completeness axiom). Sequence of real numbers, Series. Functions of one variable: differentiation and integration. Complex numbers . Differential equations:generalities. Cauchy problem for differential equations. Linear differential equations. Elements of Topology in the plane. Functions of several variables : differentiation .

Adopted texts

N. Fusco - P. Marcellini - C. Sbordone.
Elementi di Analisi Matematica uno e due ed. Liguori.
L. Cosimi - M.R. Lancia.
Complementi ed Esercizi di Analisi Matematica e Geometria Analitica,
ed. Esculapio.
M.R. Lancia - S. Marconi. Esercizi di Analisi Matematica, ed. LaDotta 2020.
M.R. Lancia - S. Marconi.Temi d’esame di Analisi Matematica, ed. LaDotta.

Prerequisites

Cfr. Syllabus Unione matematica Italiana

Exam modes

The first part of the exam consists in a written test with 4 exercises and a question on the main definitions and theorems with proofs.
To pass the test the student must solve two exercises and answer the question about the theory. The correct solution of the two exercises is necessary in order to evaluate the theorethical part.
The second part of the exam is an oral exam. All the students who, ( even though in the written test have solved two exercises), show not to have the appropriate language and skills will be asked to sit an oral exam as well as those students who whish to sit the oral examination if they have passed the exercises test.