# 00013 - Mathematical Analysis

### Course Unit Page

• Teacher Marco Mughetti

• Credits 12

• SSD MAT/05

• Language Italian

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda. ## Learning outcomes

At the end of the course, the student knows the basic tools of mathematical analysis such as real numbers, limits, continuity, derivatives and integrals.
Moreover, he can use these tools for studying other disciplines.

## Course contents

The number sets: N,Z,Q,R.
The induction principle.
Sequences of real numbers.

Differential calculus for functions of one real variable.
Exponential and logarithmic functions. Trigonometric funtions.
Limits. Continuity (local and global properties).
Derivatives, monotony. Local maxima and local minima.
Infinite and infinitesimal asymptotics. Taylor's formula.

Integral calculus for function of one real variable: primitive and integral, techniques of integration (by parts, by substitution), integral of rational functions. Generalized integrals.

An introduction to differential calculus for function of several variables. Continuity and derivatives for functions of two real variables.
Integral calculus for function of two real variables.

Bertsch, Dal Passo, Giacomelli - Analisi matematica (McGraw-Hill)
Bramanti, Pagani, Salsa  Matematica (Zanichelli)
Salsa, Squellati - Esercizi di Matematica I(Zanichelli)
Salsa, Squellati - Esercizi di Matematica II (Zanichelli)

## Teaching methods

During the lectures, the teacher explains the main topics of the theory, provides examples and shows how to solve several exercises.

## Assessment methods

The exam aims to verify the reaching of the following didactical goals:

-knowledge of basic notions of mathematical analysis
-ability in using these notions in solving exercises and problems

The exam consists of two parts:

1) the first part consists of a set of exercises. Books, notes, computers and calculators are not allowed during this test.

2) the second part is focused on the theoretical aspects of the course. Only the students that have passed the first part are allowed to attend the second part.

## Teaching tools

Blackboard, video and pc.