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Mathematic and physics

A.Y. 2021/2022

Learning objectives

The course aims to provide the student with an understanding of basic mathematics and physics (equations, inequalities, systems, limits, derivatives, mechanics, thermodynamics, wave phenomena, electricity and magnetism), illustrating their relevance with concrete examples in order to solve simple exercises in which these principles are applied to specific problems.

Expected learning outcomes

The aim of the course is to make students autonomous in solving mathematical and physical problems, providing them with the basic tools necessary for this purpose.

**Lesson period:**
First semester

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

First semester

More specific information on the delivery modes of training activities for a.y. 2021-22 will be provided over the coming months, based on the evolution of the public health situation

**Course syllabus**

For the Mathematics part:

· Numeric sets;

· Operations on sets;

· Direct and inverse proportionality;

· Percentages;

· Radicals;

· Logarithms;

· Exponentials;

· First degree integer and fractional equations;

· Whole and fractional second degree equations;

· Equations of degree higher than the second;

· Integer and fractional systems of first degree equations;

· Integer and fractional systems of second degree equations;

· Whole and fractional first degree inequalities;

· Whole and fractional second degree inequalities;

· Systems of first degree integer and fractional inequalities;

· Systems of integer and fractional second degree inequalities;

· Elements of trigonometry;

· Limits;

· Derivatives;

· Elements of mathematical logic;

· Algorithms;

For the Physics part:

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

· Kinematics: speed and acceleration (average and instantaneous); uniform rectilinear motion; uniformly accelerated motion; uniform circular motion and harmonic motion; parabolic motion.

· Dynamics of the material point: the three principles of dynamics (with practical applications); examples of forces: weight force, elastic force, constraint force, friction force; momentum; moment of a force; levers.

· 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.

· States of aggregation of matter: outline of intermolecular forces; qualitative description of the gaseous, liquid and solid states.

· States and dynamics of liquids: pressure; Pascal's law; Stevino's law; Archimedes' principle; scope; Bernoulli's theorem and its applications

· Thermodynamics: heat and temperature; mode of heat transmission; changes of state; thermal capacity and specific heat; particular transformations of a gas (isobar, isochore, isothermal and cyclic); equation of state for ideal gases; work of compression and expansion of a gas; internal energy; first and second law of thermodynamics; thermodynamic cycles; efficiency of a thermal machine.

· Electricity: electric charge and Coulomb's law; electric field of a point charge; electric field flux and Gauss' theorem; electric potential and electric potential energy; direct electric current; Ohm's laws; Kirchhoff's laws; solving electrical circuits.

· Magnetism: fundamental magnetic phenomena (wire crossed by current, coil and solenoid).

· Numeric sets;

· Operations on sets;

· Direct and inverse proportionality;

· Percentages;

· Radicals;

· Logarithms;

· Exponentials;

· First degree integer and fractional equations;

· Whole and fractional second degree equations;

· Equations of degree higher than the second;

· Integer and fractional systems of first degree equations;

· Integer and fractional systems of second degree equations;

· Whole and fractional first degree inequalities;

· Whole and fractional second degree inequalities;

· Systems of first degree integer and fractional inequalities;

· Systems of integer and fractional second degree inequalities;

· Elements of trigonometry;

· Limits;

· Derivatives;

· Elements of mathematical logic;

· Algorithms;

For the Physics part:

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

· Kinematics: speed and acceleration (average and instantaneous); uniform rectilinear motion; uniformly accelerated motion; uniform circular motion and harmonic motion; parabolic motion.

· Dynamics of the material point: the three principles of dynamics (with practical applications); examples of forces: weight force, elastic force, constraint force, friction force; momentum; moment of a force; levers.

· 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.

· States of aggregation of matter: outline of intermolecular forces; qualitative description of the gaseous, liquid and solid states.

· States and dynamics of liquids: pressure; Pascal's law; Stevino's law; Archimedes' principle; scope; Bernoulli's theorem and its applications

· Thermodynamics: heat and temperature; mode of heat transmission; changes of state; thermal capacity and specific heat; particular transformations of a gas (isobar, isochore, isothermal and cyclic); equation of state for ideal gases; work of compression and expansion of a gas; internal energy; first and second law of thermodynamics; thermodynamic cycles; efficiency of a thermal machine.

· Electricity: electric charge and Coulomb's law; electric field of a point charge; electric field flux and Gauss' theorem; electric potential and electric potential energy; direct electric current; Ohm's laws; Kirchhoff's laws; solving electrical circuits.

· Magnetism: fundamental magnetic phenomena (wire crossed by current, coil and solenoid).

**Prerequisites for admission**

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

**Teaching methods**

Frontal lessons, practise

**Teaching Resources**

Material produced in class (for the part of Mathematics)

Serway and Jevett, Principles of Physics, vol. 1 (EdiSES) (for the Physics part)

Serway and Jevett, Principles of Physics, vol. 1 (EdiSES) (for the Physics part)

**Assessment methods and Criteria**

Written exam (90 minutes) with possible intermediate test for attending students (for maths).

The exam consists in carrying out a written test aimed at ascertaining the acquisition, correct understanding and the ability to rework the course contents. The test will be evaluated out of thirty and the mark will take into account the accuracy and quality of the answers (for the Physics part).

The final grade of the exam is the arithmetic average of the marks obtained in the mathematics module and in the physics module.

The exam consists in carrying out a written test aimed at ascertaining the acquisition, correct understanding and the ability to rework the course contents. The test will be evaluated out of thirty and the mark will take into account the accuracy and quality of the answers (for the Physics part).

The final grade of the exam is the arithmetic average of the marks obtained in the mathematics module and in the physics module.

Matematica e statistica

MAT/01 - MATHEMATICAL LOGIC

MAT/02 - ALGEBRA

MAT/03 - GEOMETRY

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS

MAT/05 - MATHEMATICAL ANALYSIS

MAT/06 - PROBABILITY AND STATISTICS

MAT/07 - MATHEMATICAL PHYSICS

MAT/08 - NUMERICAL ANALYSIS

MAT/09 - OPERATIONS RESEARCH

MAT/02 - ALGEBRA

MAT/03 - GEOMETRY

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS

MAT/05 - MATHEMATICAL ANALYSIS

MAT/06 - PROBABILITY AND STATISTICS

MAT/07 - MATHEMATICAL PHYSICS

MAT/08 - NUMERICAL ANALYSIS

MAT/09 - OPERATIONS RESEARCH

Lessons: 48 hours

Professor:
Agazzi Federico Mario

Principi di fisica

FIS/01 - EXPERIMENTAL PHYSICS

FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS

FIS/03 - PHYSICS OF MATTER

FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS

FIS/05 - ASTRONOMY AND ASTROPHYSICS

FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM

FIS/07 - APPLIED PHYSICS

FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS

FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS

FIS/03 - PHYSICS OF MATTER

FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS

FIS/05 - ASTRONOMY AND ASTROPHYSICS

FIS/06 - PHYSICS OF THE EARTH AND OF THE CIRCUMTERRESTRIAL MEDIUM

FIS/07 - APPLIED PHYSICS

FIS/08 - PHYSICS TEACHING AND HISTORY OF PHYSICS

Lessons: 32 hours

Professor:
Ravizza Antonella

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