#
Mathematics and Physics

A.Y. 2019/2020

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

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

First semester

**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**

Lectures

Significant figures, scientific notation, rounding numbers (1 hour)

Percents, ratios, fractions, proportions (1 hour)

Linear and quadratic equations (2 hours)

Systems of linear equations (1 our)

Functions, derivatives and graphic representation (1 hour)

Populations and samples. Type of statistic variables. Absolute and relative frequencies. Frequency distributions (3 hours)

Descriptive statistics: Mean. Median. Mode. Measures of dispersion: deviance, variance, standard deviation, coefficient of variation, range (2 hours)

Probability. Probability distributions (2 hours)

Comparing proportions. Binomial distribution. Poisson distribution (2 hours).

Normal distribution: Standardized variable (z), standard normal distribution table,. Asimmetry and kurtosis (3 hours)

Sampling distribution of a mean. The confidence interval of a mean. The sampling distribution of a proportion. Student's t-distribution. Comparison between two means (4 hours)

Hypothesis testing: Type I and TYPE II errors (2 hours)

The Chi-squared test. Contingency tables (2 hours)

Covariance. Correlation. Linear regression. (3 hours)

Analysis of variance (ANOVA): partioning of total sum of squares. The F-test. (2 hours)

Practice

- mathematics (2 hours)

- descriptive statistics (2 hours)

- normal distribution (2 hours)

- correlation and regression (2 hours)

- analysis of variance (2 hours)

- sampling distribution (3 hours)

- proportion, Chi-squared test (3 hours)

Significant figures, scientific notation, rounding numbers (1 hour)

Percents, ratios, fractions, proportions (1 hour)

Linear and quadratic equations (2 hours)

Systems of linear equations (1 our)

Functions, derivatives and graphic representation (1 hour)

Populations and samples. Type of statistic variables. Absolute and relative frequencies. Frequency distributions (3 hours)

Descriptive statistics: Mean. Median. Mode. Measures of dispersion: deviance, variance, standard deviation, coefficient of variation, range (2 hours)

Probability. Probability distributions (2 hours)

Comparing proportions. Binomial distribution. Poisson distribution (2 hours).

Normal distribution: Standardized variable (z), standard normal distribution table,. Asimmetry and kurtosis (3 hours)

Sampling distribution of a mean. The confidence interval of a mean. The sampling distribution of a proportion. Student's t-distribution. Comparison between two means (4 hours)

Hypothesis testing: Type I and TYPE II errors (2 hours)

The Chi-squared test. Contingency tables (2 hours)

Covariance. Correlation. Linear regression. (3 hours)

Analysis of variance (ANOVA): partioning of total sum of squares. The F-test. (2 hours)

Practice

- mathematics (2 hours)

- descriptive statistics (2 hours)

- normal distribution (2 hours)

- correlation and regression (2 hours)

- analysis of variance (2 hours)

- sampling distribution (3 hours)

- proportion, Chi-squared test (3 hours)

**Teaching methods**

Lectures and Theoretical exercises

**Teaching Resources**

1) Slids of lectures are avalaible on the Ariel site [https://rrizzimf.ariel.ctu.unimi.it/v5/home/Default.aspx]

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

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

Other reference material:

4) Petrie A.,Watson P. Statistics for veterinary and animal science - Blackwell Publishing, 2011

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

6) http://minimat.ariel.ctu.unimi.it/ (progetto accessibile in ARIEL previa registrazione).

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

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

Other reference material:

4) Petrie A.,Watson P. Statistics for veterinary and animal science - Blackwell Publishing, 2011

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

6) http://minimat.ariel.ctu.unimi.it/ (progetto accessibile in ARIEL previa registrazione).

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

Professor(s)