# MATHEMATICS 1 A - L

**Academic Year 2021/2022**- 1° Year

**Teaching Staff:**

**Raffaela Giovanna CILIA**

**Credit Value:**9

**Scientific field:**MAT/05 - Mathematical analysis

**Taught classes:**42 hours

**Exercise:**36 hours

**Term / Semester:**1°

## Learning Objectives

The objectives of the course are the following:

**Knowledge and understanding: **the student will learn some basic mathematical concepts and will develop both computing ability and the capacity of manipulating some common mathematical structures among which limits and derivatives for functions of real variable, series of numbers.

**Applying knowledge and understanding: **by examples related to applied sciences, the student will learn the central role of Mathematics within science and not only as an abstract topic. This will expand the cultural horizon. He will learn the fundamental techniques and will be able to apply them in some simple problems.

**Making judgements:** the student will reflect on the meaningful methods of Mathematics to sharpe his logical ability. Many proofs will be exposed in an intuitive and schematic way, to make them more usable also to students that are not committed to Mathematics.

**Communication skills**: studying Mathematics and dedicating time to guided exercitations and seminars, the studente will learn to communicate with clarity and rigour both, verbally and in writing. The student will learn that using a properly structured language is the key point to clear and effective scientific, and non-scientific, communication.

**Learning skills: **the students, in particular the more willing, will be stimulated to examine in depth some arguments, alone or working in group.

## Course Structure

the course is organized by lectures and practices. If necessary, the telematic way will be adopted. Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus. Learning assessment may also be carried out online, should the conditions require it.

## Detailed Course Content

Systems of linear equations.

Elements of vector calculus.

Analytic geometry in the plane

Numerical Sets: excursus from the set of natural numbers to the set of real numbers. Fundamental properties of the real set numbers. Some notions of topology in R and in R^2

Sequence of real numbers.

Numerical series: character of a serie, series with positive terms. Leibnitz 's Theorem. Absolute convergence.

Real valued functions of real variable and their limits. .Continuity. Monotony. Inverse functions. Composition of functions

Differential calculus for real valued functions of one real variable and its applications Rules of derivations. Derivability of the geometri point of view. Local and global extremes. Fermat's Theorem, Rolle's Theorem. Lagrange's Theorem and applications. Convex functions. Taylor's Formula.

## Textbook Information

1) Giovanni Emmanuele Analisi Matematica I Pitagora editore

2) M. Bramanti, C.D. Pagani, S. Salsa: *Matematica - calcolo infinitesimale e algebra lineare, *ed. Zanichelli

3) S. Salsa, A. Squellati: *Esercizi di Matematica 1, *ed. Zanichelli

4) Cento pagine di algebra lineare.

5) Cento pagine di geometria analitica nel piano.

Programmazione del corso