CODE 114429 2024/2025 6 cfu anno 1 INGEGNERIA MECCANICA 8784 (L-9) - LA SPEZIA MAT/05 LA SPEZIA 1° Semester

## OVERVIEW

The aim of the course is to provide basic knowledge preparatory to other courses that require mathematical methods and tools.

## AIMS AND CONTENT

### LEARNING OUTCOMES

The knowledge of mathematical basic tools useful in physical problems modelling. The skill of setting up and solving problems by using intuitive and deductive reasoning as well as recognizing and using the suitable mathematical tools in solving problems in a physical setting. At the end of the course the student will be able 1. to state the concepts ( theorems and deﬁnitions ) introduced during the course ( f.i. Inﬁmum and Supremum of a set, continuity and differentiability of a function ); 2. to give physical and geometric interpretation of the basic concepts of Mathematical Analysis; 3. to select the suitable mathematical tools in problem solving; 4. to solve problems with deductive reasoning.

### AIMS AND LEARNING OUTCOMES

The knowledge of mathematical basic tools useful in physical problems modelling.  The skill of setting up and solving problems by using intuitive and deductive reasoning as well as recognizing and using the suitable mathematical tools in solving problems in a physical setting.

At the end of the course the student will be able

1. to state the concepts ( theorems and definitions ) introduced during the course ( f.i. Infimum and Supremum of a set, derivative, integral, line integral, Existence and Uniqueness theorems for differential problems );

2. to give physical and geometric interpretation of the basic concepts of Mathematical Analysis;

3. to set up problem solving with an intuitive approach;

4. to select the suitable mathematical tools in problem solving;

5. to solve problems with deductive reasoning.

### PREREQUISITES

Elementary Algebra, Trigonometry and Analytic Geometry in the plane.

### TEACHING METHODS

The course consists of 52 hours of lectures and practices. In the lectures the topics of the syllabus are explained with definitions and theorems and some proofs which can be useful for the comprehension of the topics and to develop the logical and deductive skills. Every theoretical topic is explained with easy examples and some exercises. In the practices, many exercises are solved with the aim of going into the knowledge of theoretical topics treated in the lectures and preparing the student for the exam. Several intermediate tests are provided.

Students  have several exercises at their disposal on Aulaweb.

Students with SLD, disability or other regularly certified special educational needs are advised to contact the professor and the University referent at the beginning of the course to agree on teaching methods that, in compliance with the course objectives, take into account the individual learning requirements.

### SYLLABUS/CONTENT

Real numbers and the real line. Cartesian coordinates in the plane. Sequences: properties and elementary examples. Functions and their graphs. Limits and continuity. Theorems about continuous functions. The derivative. Differentiation rules: product, reciprocal, quotient and chain rule. Monotone functions: the inverse function theorem. Derivatives of some elementary functions. Theorems about differentiable functions: Rolle, Lagrange, Cauchy. Higher order derivatives. Extreme values, convexity and inflection. Sketching the graph of a function. L’Hopital’s rule.  Taylor’ formula and its applications.

Main books

T. Zolezzi: Dispense di analisi matematica I.
C. Canuto – A. Tabacco: Analisi Matematica 1. Teoria ed esercizi.
Unitext, Springer – Verlag. 2014
F. Parodi – T. Zolezzi: Appunti di analisi matematica. ECIG, 2002
R. Adams: Calcolo differenziale I. Funzioni di una variabile reale. Casa ed. Ambrosiana, 1992.

Practices

M. Baronti – F. De Mari – R. van der Putten – I. Venturi: Calculus Problems. Springer 2016
M. Pavone: Temi svolti di analisi matematica I.
Marcellini-Sbordone: Esercitazioni di matematica, I volume
S. Salsa – A. Squellati: Esercizi di Matematica, volume 1.

## LESSONS

### LESSONS START

Lessons start on Thursday, 26 september 2024

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

The exam consists of a multiple choice test and a written examination. It is necessary to be successful in the multiple choice test in order to access the written exam.

To enroll the exam you must register by the deadline on the website https://servizionline.unige.it/studenti/esami/prenotazione

Students with SLD, disability or other regularly certified special educational needs are advised to contact the professor and the University referent at least 15 days before each examination to agree on exhamination methods that, in compliance with the course objectives, take into account the individual learning requirements.

### ASSESSMENT METHODS

The aim of the examination is verifying the skills acquired by the student.

As regards the Multiple choice tests the aim is verifying the student's ability to manage mathematical notation and to carry out simple computations and simple deductive reasoning. It is necessary to be successful in the multiple choice test in order to access the written exam.

The aim of the written examination is verifying the skills acquired by the student. The problems proposed in the examination call for the choice and the application of suitable mathematical tools, besides their solution needs the skill of constructing a logical connection applying theoretical topics treated. The student must solve the exercises justifying the most important passages recalling theorems and definitions and underlying the physical and geometric interpretation of the problem.

The final evaluation depends also on the quality of the written exposition and on the ability of reasoning.