# MATHEMATICAL ANALYSIS

OVERVIEW

This is a semi-annual course, devoted to differential and integral calculus in one variable.

## AIMS AND CONTENT

LEARNING OUTCOMES

Capability in following a line of logical reasoning; understanding of the essential properties of differential and integral calculus for functions of one variable. Acquisition of a sufficient calculation ability.

AIMS AND LEARNING OUTCOMES

The main objective is to supply the fundamentals of differential and integral calculus in one variable. In particular, students are expected to develop the following skills: operations on limits and derivatives, study of functions of one variable, integral calculus (indefinite, definite and improper integrals), study of integral functions.

Teaching methods

Lectures (90 hours).

SYLLABUS/CONTENT

Real numbers, cartesian coordinates in a plane, functions of one real variable, monotonic functions, composition and invertibility of functions, elementary functions, supremum and infimum, limits of functions, limits of sequences, infinitesimal and infinite functions, continuous functions and their properties, derivatives, derivation rules, derivatives of elementary functions, sign of derivatives in the study of monotonicity and convexity, maxima and minima, theorems of Fermat, Rolle, Lagrange, de l'Hopital, Taylor expansions and applications to critical points, definite and indefinite integrals, fundamental theorem of integral calculus, integral functions, improper integrals.

RECOMMENDED READING/BIBLIOGRAPHY

M. Bramanti, C. Pagani, S. Salsa: Analisi Matematica 1, Zanichelli (2008);

T. Zolezzi: Dispense di Analisi Matematica I, edizioni ERSU (anni 90);

P. Marcellini, C. Sbordone: Esercitazioni di matematica, Liguori (1988);

F. Buzzetti, E. Grassini Raffaglio, A. Vasconi: Esercizi di analisi matematica, Masson (1989);

M. Bertsch, R. Dal Passo: Elementi di analisi matematica, Aracne (2000).

M. Baronti, F. De Mari, R. Van der Putten, I. Venturi: Calculus problems, Springer (2016).

## TEACHERS AND EXAM BOARD

**Ricevimento:** At the end of lectures or by appointment.

Exam Board

MAURIZIO CHICCO (President)

LAURA BURLANDO (President)

ADA ARUFFO

## LESSONS

Teaching methods

Lectures (90 hours).

LESSONS START

September 17, 2018

## EXAMS

Exam description

The exam consists of a written and an oral test. Furthermore, during the semester, two written tests might be delivered. The students that will pass them, will be enabled to access directly the oral exam.

Assessment methods

The exam consists of a written and an oral test. The written test is based on the resolution of problems similar to those carried out during the course. In such a test is proven the ability to solve problems relating to calculation of limits, derivatives and integrals, and study of properties of one variable functions. In the oral exam is assessed the understanding of the concepts and reasoning skills acquired by the students.

## FURTHER INFORMATION

Once the course has started, office hours for students will be decided for the period of lectures. Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teachers about the course.