#
Mathematics and Physics

A.Y. 2016/2017

Learning objectives

Undefined

Expected learning outcomes

Undefined

**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

**ATTENDING STUDENTS**

**Modulo: Principi di fisica**

**Course syllabus**

Introductory topics: physical quantities and units; order of magnitude; significant figures. Scalar and vector quantities; sum of vectors; scalar and vector product; representation of a vector by its coordinates.

Kinematics: average and istantaneous velocity; average and istantaneous acceleration; rectilinear motion at constant velocity and constant acceleration; circular motion at constant speed; parabolic motion; harmonic motion.

Dynamics of a material point: Newton's laws with applications; gravity; elastic force; vincular reactions; friction; a brief overview of the dynamics of continuum bodies and systems of several bodies; momentum; center of mass; torque; law of the lever.

Work and energy: definition of work; kinetic energy theorem; conservative forces; stable and unstable equilibria; mechanical energy conservation with applications.

States of matter: a brief overview of intermolecular forces; a qualitative descripion of gas, liquid, and solid states.

Statics and dynamics of liquids: pressure; Pascal's law; Stevin's law; Archimedes' law; flow rate; Bernoulli's theorem with applications.

Thermodynamics: internal energy; heat; temperature; modes of heat transfer; thermal capacity; equation of state of an ideal gas; expansion and compression work; first and second principles of thermodynamics; a cursory glance at entropy.

Electricity: electric charge; Coulomb's law; electric potential; electric current; resistance; Ohm's law.

Kinematics: average and istantaneous velocity; average and istantaneous acceleration; rectilinear motion at constant velocity and constant acceleration; circular motion at constant speed; parabolic motion; harmonic motion.

Dynamics of a material point: Newton's laws with applications; gravity; elastic force; vincular reactions; friction; a brief overview of the dynamics of continuum bodies and systems of several bodies; momentum; center of mass; torque; law of the lever.

Work and energy: definition of work; kinetic energy theorem; conservative forces; stable and unstable equilibria; mechanical energy conservation with applications.

States of matter: a brief overview of intermolecular forces; a qualitative descripion of gas, liquid, and solid states.

Statics and dynamics of liquids: pressure; Pascal's law; Stevin's law; Archimedes' law; flow rate; Bernoulli's theorem with applications.

Thermodynamics: internal energy; heat; temperature; modes of heat transfer; thermal capacity; equation of state of an ideal gas; expansion and compression work; first and second principles of thermodynamics; a cursory glance at entropy.

Electricity: electric charge; Coulomb's law; electric potential; electric current; resistance; Ohm's law.

**Modulo: Matematica e statistica**

**Course syllabus**

Didactics

Sets and Venn diagrams (2 hours)

Percents, ratios, fractions, proportions (1 ora)

Linear and quadratic equations (2 hours)

Systems of linear equations (1 ora)

Functions and graphic representation (1 hour)

Populations and samples. Type of statistic variables. Absolute and relative frequencies. Frequency distributions (2 hours)

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

Probability. Probability distributions (2 hours)

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

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

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

Normal distribution: Standardized variable (z), standard normal distribution table,. Asimmetry and kurtosis (2 hours)

Covariance. Correlation. Linear regression. (2 hours)

Analysis of variance (ANOVA): partioning of total sum of squares. The F-test. (2 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 (3 hours)

Experimental design (1 hour)

Logistic model. Population interaction: competition, predation, cooperation, adaptation (2 hours)

Epidemiology: incidence, prevalence, mortality. Cohort and case-control studies. The screening (6 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)

Sets and Venn diagrams (2 hours)

Percents, ratios, fractions, proportions (1 ora)

Linear and quadratic equations (2 hours)

Systems of linear equations (1 ora)

Functions and graphic representation (1 hour)

Populations and samples. Type of statistic variables. Absolute and relative frequencies. Frequency distributions (2 hours)

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

Probability. Probability distributions (2 hours)

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

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

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

Normal distribution: Standardized variable (z), standard normal distribution table,. Asimmetry and kurtosis (2 hours)

Covariance. Correlation. Linear regression. (2 hours)

Analysis of variance (ANOVA): partioning of total sum of squares. The F-test. (2 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 (3 hours)

Experimental design (1 hour)

Logistic model. Population interaction: competition, predation, cooperation, adaptation (2 hours)

Epidemiology: incidence, prevalence, mortality. Cohort and case-control studies. The screening (6 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)

**NON-ATTENDING STUDENTS**

**Modulo: Principi di fisica**

**Course syllabus**

Students who do not attend the course are expected to master all the topics covered by it

**Modulo: Matematica e statistica**

**Course syllabus**

Students who do not attend the course are expected to master all the topics covered by it

Modulo: Matematica e statistica

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

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

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

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

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

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

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

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

Practicals: 16 hours

Lessons: 32 hours

Lessons: 32 hours

Professor:
Milani Paolo

Professor(s)