#
Mathematics and Physics

A.Y. 2020/2021

Learning objectives

The purpose of the Physics unit of the Course is to illustrate the basic principles of fundamental Physics (mechanics, thermodynamics, electricity), to show their relevance by examples taken from familiar situations, and to enable students to solve some simple problems involving the applications of these principles. The course of Mathematics and Statistics is aimed at introducing students to quantitative aspects of modern biology and to the application of statistics in animal science. In order to understand the topics covered by the Course, students should have a good knowledge of elements of basic Mathematics such as fractions, powers, algebraic equations of 1st and 2nd degree, formulas for areas and volumes of simple figures and solid bodies, and the concept and graphical representation of mathematical functions.

Expected learning outcomes

The studen twill demonstrate to get the basic knowledge of the the topics covered in the course and to be able to apply, using an adequate logical process, such knowledge to the resolution of simple problems of physics and statistics

**Lesson period:** First semester
(In case of multiple editions, please check the period, as it may vary)

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

First semester

The lessons will be held on the Microsoft Teams platform and can be followed both in sync on the base of the first semester schedule and asynchronously because they will be recorded and left available to students on the same platform. Some lessons and PDF files may be available on the Ariel platform.

**Prerequisites for admission**

Basic mathematics notions are required, such as solving algebraic equations, calculating areas of plane figures and volumes of solids.

**Assessment methods and Criteria**

The exam consists of a written test with questions related to the Mathematics module and a written test with questions related to the Physics module. The two parts are carried out on the same day in separate times. The final evaluation is the arithmetic mean of the evaluations of the 2 tests.

**Modulo: Principi di fisica**

**Course syllabus**

Preliminary elements: physical quantities; unit of measure; scientific notation and orders of magnitude; significant figures; scalar quantities and vector quantities; operations with vectors (sum, subtraction, scalar product and vector product, decomposition). (2 h) + (2 h of exercises)

Kinematics: speed and acceleration (averages and snapshots); uniform straight motion; uniformly accelerated motion; uniform circular motion and harmonic motion; parabolic motion. (4 h) + (2 h of exercises)

Dynamics of the material point: the three principles of dynamics (with practical applications); examples of forces: weight force, elastic force, constraining force, friction force; momentum; moment of a force; levers. (4h) + (2 h of exercises)

Work and energy: definition of work; mechanical energy; kinetic energy and kinetic energy theorem; conservative forces; gravitational and elastic potential energy; conservation of mechanical energy and its applications. (4 h) + (2 h of exercises)

States of aggregation of matter: outline of intermolecular forces; qualitative description of gaseous, liquid and solid states. (2 h)

States and dynamics of liquids: pressure; Pascal's law; Stevino's law; principle of Archimedes; scope; Bernoulli theorem and its applications. (4 h) + (2 h of exercises)

Thermodynamics: heat and temperature; heat transmission mode; status changes; heat capacity and specific heat; particular transformations of a gas (isobars, isochores, isotherms and cyclics); equation of state of perfect gases; gas compression and expansion work; internal energy; first and second law of thermodynamics; thermodynamic cycles; efficiency of a thermal machine. (4 h) + (2 h of exercises)

Electricity: electric charge and Coulomb's law; electric field of a point charge; flow of the electric field and Gauss theorem; electrical potential and electric potential energy; continuous electric current; laws of Ohm; Kirchhoff's laws; resolution of electrical circuits. (4 h) + (2 h of exercises)

Magnetism: fundamental magnetic phenomena (current path, coil and solenoid). (4 h) + (2 h of exercises)

Kinematics: speed and acceleration (averages and snapshots); uniform straight motion; uniformly accelerated motion; uniform circular motion and harmonic motion; parabolic motion. (4 h) + (2 h of exercises)

Dynamics of the material point: the three principles of dynamics (with practical applications); examples of forces: weight force, elastic force, constraining force, friction force; momentum; moment of a force; levers. (4h) + (2 h of exercises)

Work and energy: definition of work; mechanical energy; kinetic energy and kinetic energy theorem; conservative forces; gravitational and elastic potential energy; conservation of mechanical energy and its applications. (4 h) + (2 h of exercises)

States of aggregation of matter: outline of intermolecular forces; qualitative description of gaseous, liquid and solid states. (2 h)

States and dynamics of liquids: pressure; Pascal's law; Stevino's law; principle of Archimedes; scope; Bernoulli theorem and its applications. (4 h) + (2 h of exercises)

Thermodynamics: heat and temperature; heat transmission mode; status changes; heat capacity and specific heat; particular transformations of a gas (isobars, isochores, isotherms and cyclics); equation of state of perfect gases; gas compression and expansion work; internal energy; first and second law of thermodynamics; thermodynamic cycles; efficiency of a thermal machine. (4 h) + (2 h of exercises)

Electricity: electric charge and Coulomb's law; electric field of a point charge; flow of the electric field and Gauss theorem; electrical potential and electric potential energy; continuous electric current; laws of Ohm; Kirchhoff's laws; resolution of electrical circuits. (4 h) + (2 h of exercises)

Magnetism: fundamental magnetic phenomena (current path, coil and solenoid). (4 h) + (2 h of exercises)

**Teaching methods**

Lectures and theoretical exercises

**Teaching Resources**

Serway e Jevett, Principi di fisica, vol. 1 (EdiSES)

**Modulo: Matematica e statistica**

**Course syllabus**

1. Theoretical Classes

- Samples and populations. Types of variables: qualitative, quantitative.. Absolute and relative frequency. (2 hrs)

- Diagrams and histograms, frequency distribution, cumulative frequencies, quartiles and percentiles. Box-plot. (2 hrs)

- Measures of central tendency: mean, median, mode. Measures of dispersion: range of variation, deviance, variance, standard deviation, coefficient of variation (2 hrs)

- Probability. Basic rules of probability. Discrete and continue probability distribution (2 hrs)

- Binomial distribution. Poisson distribution (3 hrs)

- Normal distribution. Standardization of a variable. Normalized standard distribution. Asymmetry and kurtosis (2 hrs)

- The central limit theorem. The sampling distribution of an estimate: the standard error. The confidence interval. Student's t-disdtribution (2 hrs).

- Verifying hypotheses. Null hypothesis and alternative statistical significance and P-value Error types I and II (2 hrs)

- Comparison between a sample mean and a population mean. Comparison between two sample means (2 hrs).

- The chi-square test. The chi-square distribution. The 2x2 contingency table (3 hrs)

- Relationship between variables: covariance. Correlation and linear regression. Regression analysis (4 hrs).

- Analysis of variance: the comparison between means of several groups:. The F-distribution (4 hrs)

2. Practical classes (Computer Classroom):

- descriptive statistics (2 hrs)

- normal distribution (2 hrs)

- correlation and regression (3 hrs)

- analysis of variance (3 hrs)

- confidence interval, comparion between means (3 hrs)

- χ2 test (3 hrs)

- Samples and populations. Types of variables: qualitative, quantitative.. Absolute and relative frequency. (2 hrs)

- Diagrams and histograms, frequency distribution, cumulative frequencies, quartiles and percentiles. Box-plot. (2 hrs)

- Measures of central tendency: mean, median, mode. Measures of dispersion: range of variation, deviance, variance, standard deviation, coefficient of variation (2 hrs)

- Probability. Basic rules of probability. Discrete and continue probability distribution (2 hrs)

- Binomial distribution. Poisson distribution (3 hrs)

- Normal distribution. Standardization of a variable. Normalized standard distribution. Asymmetry and kurtosis (2 hrs)

- The central limit theorem. The sampling distribution of an estimate: the standard error. The confidence interval. Student's t-disdtribution (2 hrs).

- Verifying hypotheses. Null hypothesis and alternative statistical significance and P-value Error types I and II (2 hrs)

- Comparison between a sample mean and a population mean. Comparison between two sample means (2 hrs).

- The chi-square test. The chi-square distribution. The 2x2 contingency table (3 hrs)

- Relationship between variables: covariance. Correlation and linear regression. Regression analysis (4 hrs).

- Analysis of variance: the comparison between means of several groups:. The F-distribution (4 hrs)

2. Practical classes (Computer Classroom):

- descriptive statistics (2 hrs)

- normal distribution (2 hrs)

- correlation and regression (3 hrs)

- analysis of variance (3 hrs)

- confidence interval, comparion between means (3 hrs)

- χ2 test (3 hrs)

**Teaching methods**

Lectures and Theoretical exercises

**Teaching Resources**

- Material provided and available on Ariel website [https://rrizzimf.ariel.ctu.unimi.it/v5/home/Default.aspx]

- Whitlock M.C., Schulter D. - Analisi statistica dei dati biologici - Ed. Zanichelli, 2010-

- Triola M.M., Triola M. F. - Fondamenti di statistica per le discipline biomediche- Pearson Italia, 2013

- Pagano M., Gauvreau K.: "Biostatistica", Ed. Idelson-Gnocchi, Milano, 2003.

- Whitlock M.C., Schulter D. - Analisi statistica dei dati biologici - Ed. Zanichelli, 2010-

- Triola M.M., Triola M. F. - Fondamenti di statistica per le discipline biomediche- Pearson Italia, 2013

- Pagano M., Gauvreau K.: "Biostatistica", Ed. Idelson-Gnocchi, Milano, 2003.

Modulo: Matematica e statistica

MAT/01 - MATHEMATICAL LOGIC - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

Practicals: 16 hours

Lessons: 32 hours

Lessons: 32 hours

Professor:
Rizzi Rita Maria

Modulo: Principi di fisica

FIS/01 - EXPERIMENTAL PHYSICS - University credits: 0

FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 0

FIS/03 - PHYSICS OF MATTER - University credits: 0

FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS - University credits: 0

FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 0

FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS - University credits: 0

FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 0

FIS/03 - PHYSICS OF MATTER - University credits: 0

FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS - University credits: 0

FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 0

FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS - University credits: 0

Practicals: 16 hours

Lessons: 32 hours

Lessons: 32 hours

Professor:
Ravizza Antonella

Educational website(s)

Professor(s)