Mathematic and physics

A.Y. 2021/2022
10
Max ECTS
80
Overall hours
SSD
FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08 MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
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.
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).
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)
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.
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
Lessons: 48 hours
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
Lessons: 32 hours
Professor: Ravizza Antonella