Corso di laurea in Scienza dei Materiali
Corso di laurea in Scienza e Tecnologia dei Materiali

Students learn to:

know the main families of functions and their properties

switch from one representation to another among: graphic, symbolic, numerical

know and apply the fundamental concepts of differential and integral calculus for functions of one and more variables, with particular regard to chemical and physical applications

apply statistics with theoretical and technical applications, through the use of software R.

The student should know the local and global properties and the graphs of the elementary functions; switch from the equation to the graph of a function and viceversa; study a function of one variable; compute properand improper integrals; solve simple ordinary differential equations of first and second order; know the equations of straight lines, planes, conics and elementary quadrics; study a function of two variables;compute double, triple and line integrals; compute integrals of differential forms; be able to apply the main results of vector analysis.

For statistics, the student should know how to describe datasets, how to infer the fundamental properties of the distributions from which dataset are sampled, and per form simple hypotheses test using R.

The course is based on 120 hours of lectures and exercises in 3 modules:

One real variable (56h), two real variables (44h), statistics (20h).

During statistics lectures, students can bring their laptop and use R.

The attendance to the course is not compulsory.

COVID emergency:

The lessons will be in presence and students can access the room if equipped with surgical masks and after having sanitized their hands. The need the GREEN PASS.

The students are invited to subscribe the course, both on the present campusnet page (at the link “Registrati al corso” at the end of this page) and on the moodle page.

The webex link for the lessons of prof.Robutti è: https://unito.webex.com/meet/ornella.robutti

The webex link for the lessons of prof. Fatibene is: https://unito.webex.com/meet/lorenzo.fatibene

Booking the exam sessions through Esse3 and within one week from the date of the exam is mandatory and essential. Students who have not booked will not be admitted. Furthermore, for a better organization of the IT laboratories, those who book and do not show up for the exam without first informing the teachers will not be entitled to participate to the next session.

To take the exam it is necessary to present an identification document (preferably the smartcard) and to remember the University credentials (username and password), which must be entered on the computer of the classroom to start the tests.

The exam consists of a test and two tests (one of Calculus and one of Statistics) carried out in computerized mode. It is not possible to withdraw after starting the tests: the test will be evaluated in any case.

During the tests the use of electronic tools is not allowed and it is not allowed to consult texts or notes. You can use the calculator available on your computer and, for the Statistics test, the software R.

It is not allowed to keep mobile phones, tablets and the like at the computer station (even if switched off, in your pocket, ..). The presence of one of these devices, even switched off, will result in immediate expulsion from the classroom and cancellation of the test.

Basic skills assessment test

The test consists of answering five multiple choice questions, which aim to verify the student's basic knowledge.

The duration is twenty minutes; to pass the test, at least 4 out of 5 questions must be answered correctly. The result is: passed or failed and is known immediately at the end of the test; those who do not pass the test cannot access the exam.

Calculus exam paper (exercises and theory)

This test focuses on the topics covered during the lessons and exercises; it consists in carrying out exercises and answering questions of a theoretical or logical-deductive nature. The test includes topics from both the Calculus I module and the Calculus II module.

The test is graded out of thirty and passed with a grade of at least 16/30.

Those who fail this test cannot access the Statistics test.

Statistics exam (exercises and theory)

This test focuses on the topics covered during the lessons and exercises; it consists in carrying out exercises and answering questions of a theoretical or logical-deductive nature.

The test is graded out of thirty and passed with a grade of at least 16/30.

The exam is passed if the average of the two tests (Calculus and Statistica) is at least equal to 18/30.

The test and all the exams (Calculus and Statistics) must be passed in the same session: in case of failure even in only one part of the exam, in subsequent sessions any parts already passed will not be taken into account and the examination in full.

Information for students with SLD

https://www.unito.it/servizi/lo-studio/studenti-con-disturbi-specifici-di-appearning-dsa/supporto-agli-studenti-con

Students from previous academic years

From January 2020 all students will have to take the exam according to the modalities of the current year.

INFORMATION AND RULES FOR EXAMINATION DURING THE PERIOD OF RESTRICTIONS DUE TO THE CORONAVIRUS EMERGENCY

Starting from the September 2020 session, except for further restrictions, the exams of the Mathematics course will be carried out in the presence, in the computerized classrooms of Palazzo Campana, in Via Carlo Alberto, 10. Students who will be able to apply for the exam online in one of the following conditions:

a) situation of fragility (direct and indirect, illness, etc.)
b) residence or domicile outside the region
c) temporary absence from the regional territory for documentable needs.

For students who will take the online exam, the following rules already in force for the summer session apply:
Students must connect to the webex meeting that will be communicated a few days before the exam, and remain connected for the entire time of the test, with microphone and camera active.
They must be able to access the institutional e-mail if requested by the teachers.
They must have an identity document.
During the test, it is possible that it is necessary to upload material online (the ugly of the exercises, or part of the performance of some exercises), therefore each student must be equipped to photograph / scan what he has written and upload it according to the modalities that will be explained during the test.
The preliminary barrier test will not be carried out, but all enrolled students will take the exam directly.
The test will be computerized, with exercises of the usual types.
After the written test, an oral interview will be carried out (according to a schedule that will be communicated after the written test) in which an exercise will be chosen from those carried out in the written test, and each student will have to explain how they did the exercise and what they are, the reasons for the answers he gave. This interview is not carried out for evaluation purposes but is an integral part of the written test and should be considered as a clarification. It aims to give the right weight to any errors that are also the result of the unusual way.

The tutoring activity will be on Monday from 2 to 4 pm on site.

Real functions of one variable (56h). 

• Domain, properties and graphics of elementary functions. Limits, continuity and asymptotic lines. Derivatives, maxima, minima, inflection points. Differential and Taylor's expansion.
• Integrals of funtions of one variable. Definite and indefinite integrals. Main methods of integration.
• Ordinary  differential equations. Separable and linear first order differential equations. Linear second order differential equations.

Real functions of two variables (44h). 

• Complex numbers. Algebraic, trigonometric and exponential form of a complex number.
• Domain, limits, continuity, partial derivatives, stationary points and extrema.
• Integrals of functions of several variables. Double and triple integrals, line and surface integrals. Theorems of Green, Gauss and Stokes.

Statistics (20h)

• Introduction to R, Random qualitative and quantitative samples, univariate and bivariate. Position and spread indices, graphic representation of datasets (hist, boxplot, scatterplot, boxplot). Qualitative comparison of datasets, independence and correlation measures. Tables for bivariate datasets.
• Probability: elementary probability, random variables, mean, variance. Sampling statistics and distribution. Examples of distributions.
• Inferential statistics: variance test, estimate intervals proportions, mean, variance, for differences, non-parametric median. Hypothesis tests for proportions, mean, median. Test for two (dependent and independent) samples