22455 - Lab-based Course on Mechanics and Thermodynamics (M-Z)

Learning outcomes

The purpose of this course is to provide an introduction to probability and statistics useful in the analysis of experimental data. Students are expected to be able to correctly measure physical quantities, analyse data taken during laboratory sessions and write short reports.

Course contents

Module 1

The measure of physical quantities

the experimental method; the International System (SI) of units; the experimental uncertanties (statistical and systematic errors); the Gauss distribution; the maximum likelihood method for the estimation of the parameters of a distribution; linear fits; rejection of data; the Student distribution; confidence intervals and confidence levels; the binomial and poissoninan disrtibution; the chi2 test.

Introduction to data acquisition based on electronic devices and personal computer

sensors and transducers; analog and digital signals; resolution, amplification, code width.

Statistics and probability

Basic elements of probability; random cariables; probability density functions; binomial, poisson, uniform, normale and gaussian distributions; mean and variance; covariance and correlation coefficient; confidence level; chauvenet thoerem; student distribution; maximum likelihood criterion; least squared method; weighted mean; linear regression; chi squared distribution; best fit; hypothesis tests and null hypothesis; 

Experiment performed in laboratory

1) measurement of the inertia of a solid body;

2) calibration of a thermocouple;

3) linear and angular momentum conservation;

4) Ruchardt and Perrin experiments;

Experiments 3) and 4) are part of Moduls 2, 4 and 5

Data analysis could be performed using statistical function of software package ROOT.

Module 3

ROOT framework for data analysis

- User interface

- Representation of experimental data with ROOT: histograms, canvas and related commands;

- Monte Carlo generators;

- Examples of uniform, gaussina, exponential and gaussian distribution;

- Examples of ROOT macros for data aquired during laboratory sessions.

Readings/Bibliography

P. Fornasini "The uncertainty in physical measurements" Springer.

J. R. Tayor "Introduzione all'analisi degli errori" (seconda edizione)
Zanichelli.

Teaching methods

Lectures and laboratory sessions.

Assessment methods

Written examination consisting of 3 exercises on statistical method and 1 exercise on ROOT data analysis framework.

Oral examination consisting on the discussion of one experience performed in the laboratory sessions and 2 questions on statistical theory.

Teaching tools

Slides

Office hours

See the website of Sara Valentinetti

See the website of Nicolò Jacazio

See the website of Silvia Arcelli

See the website of Silvia Arcelli