Course program
* Introduction, mathematical and statistical elements (5 hours)
1. Classical and quantum physics. Scientific method. Physical laws. Physical quantities, fundamental and derived quantities. Dimensional analysis. International system, units of mass, length, time. Scientific notation, orders of magnitude. Equivalences.
2. Probability and statistical analysis. Descriptive statistics: basic definitions, experimental distributions of data and their representation. Probability: definitions. Random variables and main distributions (uniform, binomial, Poissonian, Gaussian). Expected value, variance.
3. Measurement errors. Absolute and relative error. Systematic errors. Single measure result. Result of many measurements, mean and mean squared error. Significant digits.
4. Reference systems. Cartesian and polar coordinates. Trigonometry: sine, cosine, tangent.
5. Scalars and vectors. Operations with vectors, addition and subtraction, scalar and vector product.
6. Review of differential and integral calculus.
* Mechanics (28 hours)
7. Kinematics. Material point, position, displacement, time law, average speed. Instantaneous speed as a limit of the average speed and as a derivative of the time law. Geometric interpretation. Average and instantaneous acceleration. Uniform rectilinear motion. Uniformly accelerated motion. Motion of a body in free fall. Finding position from velocity and velocity from acceleration.
8. Projectile motion: trajectory, range, maximum height. Normal and tangential acceleration, Uniform circular motion.
9. Forces. First, second and third law of dynamics. Inertial and non-inertial systems. Law of universal gravitation, force of gravity on earth. Notes of forces in nature. Binding reactions. Normal reaction, static and dynamic friction force, resistance forces of the medium, tension of a rope. Inclined plane with and without friction. The elastic force. Harmonic motion. Simple pendulum. Centripetal force. The apparent forces (centrifugal force and hints).
10. Work of a force. Work of the weight force, of the elastic force, of the dynamic friction force. Kinetic energy and kinetic energy theorem. Power. Conservative and non-conservative forces. Potential energy, relationship between force and potential energy. Potential energy of the gravitational field, of the harmonic oscillator. Law of conservation of mechanical energy. Escape velocity from earth. Mechanical energy in the presence of conservative forces.
11. Momentum. Impulse of a force. First cardinal equation of a material point system. Law of conservation of momentum. Collisions. Central elastic collisions. Inelastic collisions. Totally inelastic collisions.
12. Properties of fluids. Density and pressure. Stevino's law. Pascal's law. Communicating vessels. Torricelli barometer. Archimedes' principle. Applications to the circulatory system. Fluids in motion. Flow rate. Bernoulli equation. Venturi effect, law of outflow. Real fluids. Viscosity and Poiseuille's law (notes). Surface tension and Laplace's law (notes).
* Thermodynamics (8 hours)
13. Thermodynamic system. State variables. Thermodynamic equilibrium. Zeroth law of thermodynamics. Temperature. Thermal expansion. Mercury thermometer. Gas thermometer. Celsius and Fahrenheit scale. Absolute temperature. Thermodynamic transformations. Gay-Lussac and Boyle-Mariotte laws. Perfect gases. Equations of state of perfect gases. Kinetic theory of gases. Microscopic interpretation of pressure and temperature. Principle of equipartition of energy.
14. Heat. Thermal capacity and specific heat of solids and liquids. Molar specific heat. Equilibrium temperature. Changes of state and latent heat. Evaporation and boiling. Heat transfer, conduction, convection and radiation.
15. Work in thermodynamic transformations. Work in the PV plan. Work in isochoric transformations, reversible isobars, reversible isotherms of an ideal gas. First law of thermodynamics. Internal energy. Free expansion of an ideal gas. Internal energy of an ideal gas. Molar specific heats of an ideal gas. Reversible adiabatic transformations of an ideal gas.
16. Thermal machines, refrigeration machines, heat pumps. Performance and COP. Carnot machine. Second law of thermodynamics, Clausius and Kelvin statements. Entropy. Entropy and disorder.
* Electromagnetism (19 hours)
17. Electrical phenomena, electric charge, charge density. Conductors and insulators. Induction and polarization. Coulomb's law. Electric force and field, superposition principle, field of a point charge. Electric dipole. Electric field lines. Motion of an electron in a uniform electric field. Electric field flux, Gauss theorem. Uniformly charged sphere, infinite flat plate, double layer.
18. Electrostatic potential, electrostatic potential energy. Potential of a point electric charge. Potential difference in a uniform electric field.
19. Conductors in electrostatic equilibrium. Coulomb theorem, point effect. Charged conducting sphere. Electrostatic screen. Electric capacity. Condensers, plane condenser. Energy stored in a capacitor. Energy density of the electric field. Dielectric filled capacitor.
20. Direct electric current, drift velocity, current density. Electric resistance, Ohm's laws. Joule effect.
21. Magnetic phenomena, magnetic field. Force on a wire carrying a current in an external magnetic field. Lorentz force. Motion of a charge in a uniform magnetic field with velocity perpendicular to the field. Speed selector and mass spectrometer. Magnetic field generated by a current-carrying wire. Biot-Savart law. Magnetic field generated by a circular coil (in the center) carrying current. Gauss's theorem for the magnetic field. Faraday's law. Lenz's law.
* Introduction, mathematical and statistical elements
1. Classical and quantum physics. Scientific method. Physical laws. Physical quantities, fundamental and derived quantities. Dimensional analysis. International system, units of mass, length, time. Scientific notation, orders of magnitude. Equivalences.
2. Probability and statistical analysis. Descriptive statistics: basic definitions, experimental distributions of data and their representation. Probability: definitions. Random variables and main distributions (uniform, binomial, Poissonian, Gaussian). Expected value, variance.
3. Measurement errors. Absolute and relative error. Systematic errors. Single measure result. Result of many measurements, mean and mean squared error. Significant digits.
4. Reference systems. Cartesian and polar coordinates. Trigonometry: sine, cosine, tangent.
5. Scalars and vectors. Operations with vectors, addition and subtraction, scalar and vector product.
6. Review of differential and integral calculus.
* Mechanics
7. Kinematics. Material point, position, displacement, time law, average speed. Instantaneous speed as a limit of the average speed and as a derivative of the time law. Geometric interpretation. Average and instantaneous acceleration. Uniform rectilinear motion. Uniformly accelerated motion. Motion of a body in free fall. Finding position from velocity and velocity from acceleration.
8. Projectile motion: trajectory, range, maximum height. Normal and tangential acceleration, Uniform circular motion.
9. Forces. First, second and third law of dynamics. Inertial and non-inertial systems. Law of universal gravitation, force of gravity on earth. Notes of forces in nature. Binding reactions. Normal reaction, static and dynamic friction force, resistance forces of the medium, tension of a rope. Inclined plane with and without friction. The elastic force. Harmonic motion. Simple pendulum. Centripetal force. The apparent forces (centrifugal force and hints).
10. Work of a force. Work of the weight force, of the elastic force, of the dynamic friction force. Kinetic energy and kinetic energy theorem. Power. Conservative and non-conservative forces. Potential energy, relationship between force and potential energy. Potential energy of the gravitational field, of the harmonic oscillator. Law of conservation of mechanical energy. Escape velocity from earth. Mechanical energy in the presence of conservative forces.
11. Momentum. Impulse of a force. First cardinal equation of a material point system. Law of conservation of momentum. Collisions. Central elastic collisions. Inelastic collisions. Totally inelastic collisions.
12. Properties of fluids. Density and pressure. Stevino's law. Pascal's law. Communicating vessels. Torricelli barometer. Archimedes' principle. Applications to the circulatory system. Fluids in motion. Flow rate. Bernoulli equation. Venturi effect, law of outflow. Real fluids. Viscosity and Poiseuille's law (notes). Surface tension and Laplace's law (notes).
* Thermodynamics
13. Thermodynamic system. State variables. Thermodynamic equilibrium. Zeroth law of thermodynamics. Temperature. Thermal expansion. Mercury thermometer. Gas thermometer. Celsius and Fahrenheit scale. Absolute temperature. Thermodynamic transformations. Gay-Lussac and Boyle-Mariotte laws. Perfect gases. Equations of state of perfect gases. Kinetic theory of gases. Microscopic interpretation of pressure and temperature. Principle of equipartition of energy.
14. Heat. Thermal capacity and specific heat of solids and liquids. Molar specific heat. Equilibrium temperature. Changes of state and latent heat. Evaporation and boiling. Heat transfer, conduction, convection and radiation.
15. Work in thermodynamic transformations. Work in the PV plan. Work in isochoric transformations, reversible isobars, reversible isotherms of an ideal gas. First law of thermodynamics. Internal energy. Free expansion of an ideal gas. Internal energy of an ideal gas. Molar specific heats of an ideal gas. Reversible adiabatic transformations of an ideal gas.
16. Thermal machines, refrigeration machines, heat pumps. Performance and COP. Carnot machine. Second law of thermodynamics, Clausius and Kelvin statements. Entropy. Entropy and disorder.
* Electromagnetism
17. Electrical phenomena, electric charge, charge density. Conductors and insulators. Induction and polarization. Coulomb's law. Electric force and field, superposition principle, field of a point charge. Electric dipole. Electric field lines. Motion of an electron in a uniform electric field. Electric field flux, Gauss theorem. Uniformly charged sphere, infinite flat plate, double layer.
18. Electrostatic potential, electrostatic potential energy. Potential of a point electric charge. Potential difference in a uniform electric field.
19. Conductors in electrostatic equilibrium. Coulomb theorem, point effect. Charged conducting sphere. Electrostatic screen. Electric capacity. Condensers, plane condenser. Energy stored in a capacitor. Energy density of the electric field. Dielectric filled capacitor.
20. Direct electric current, drift velocity, current density. Electric resistance, Ohm's laws. Joule effect.
21. Magnetic phenomena, magnetic field. Force on a wire carrying a current in an external magnetic field. Lorentz force. Motion of a charge in a uniform magnetic field with velocity perpendicular to the field. Speed selector and mass spectrometer. Magnetic field generated by a current-carrying wire. Biot-Savart law. Magnetic field generated by a circular coil (in the center) carrying current. Gauss's theorem for the magnetic field. Faraday's law. Lenz's law.
* Introduction, mathematical and statistical elements
1. Classical and quantum physics. Scientific method. Physical laws. Physical quantities, fundamental and derived quantities. Dimensional analysis. International system, units of mass, length, time. Scientific notation, orders of magnitude. Equivalences.
2. Probability and statistical analysis. Descriptive statistics: basic definitions, experimental distributions of data and their representation. Probability: definitions. Random variables and main distributions (uniform, binomial, Poissonian, Gaussian). Expected value, variance.
3. Measurement errors. Absolute and relative error. Systematic errors. Single measure result. Result of many measurements, mean and mean squared error. Significant digits.
4. Reference systems. Cartesian and polar coordinates. Trigonometry: sine, cosine, tangent.
5. Scalars and vectors. Operations with vectors, addition and subtraction, scalar and vector product.
6. Review of differential and integral calculus.
* Mechanics
7. Kinematics. Material point, position, displacement, time law, average speed. Instantaneous speed as a limit of the average speed and as a derivative of the time law. Geometric interpretation. Average and instantaneous acceleration. Uniform rectilinear motion. Uniformly accelerated motion. Motion of a body in free fall. Finding position from velocity and velocity from acceleration.
8. Projectile motion: trajectory, range, maximum height. Normal and tangential acceleration, Uniform circular motion.
9. Forces. First, second and third law of dynamics. Inertial and non-inertial systems. Law of universal gravitation, force of gravity on earth. Notes of forces in nature. Binding reactions. Normal reaction, static and dynamic friction force, resistance forces of the medium, tension of a rope. Inclined plane with and without friction. The elastic force. Harmonic motion. Simple pendulum. Centripetal force. The apparent forces (centrifugal force and hints).
10. Work of a force. Work of the weight force, of the elastic force, of the dynamic friction force. Kinetic energy and kinetic energy theorem. Power. Conservative and non-conservative forces. Potential energy, relationship between force and potential energy. Potential energy of the gravitational field, of the harmonic oscillator. Law of conservation of mechanical energy. Escape velocity from earth. Mechanical energy in the presence of conservative forces.
11. Momentum. Impulse of a force. First cardinal equation of a material point system. Law of conservation of momentum. Collisions. Central elastic collisions. Inelastic collisions. Totally inelastic collisions.
12. Properties of fluids. Density and pressure. Stevino's law. Pascal's law. Communicating vessels. Torricelli barometer. Archimedes' principle. Applications to the circulatory system. Fluids in motion. Flow rate. Bernoulli equation. Venturi effect, law of outflow. Real fluids. Viscosity and Poiseuille's law (notes). Surface tension and Laplace's law (notes).
* Thermodynamics
13. Thermodynamic system. State variables. Thermodynamic equilibrium. Zeroth law of thermodynamics. Temperature. Thermal expansion. Mercury thermometer. Gas thermometer. Celsius and Fahrenheit scale. Absolute temperature. Thermodynamic transformations. Gay-Lussac and Boyle-Mariotte laws. Perfect gases. Equations of state of perfect gases. Kinetic theory of gases. Microscopic interpretation of pressure and temperature. Principle of equipartition of energy.
14. Heat. Thermal capacity and specific heat of solids and liquids. Molar specific heat. Equilibrium temperature. Changes of state and latent heat. Evaporation and boiling. Heat transfer, conduction, convection and radiation.
15. Work in thermodynamic transformations. Work in the PV plan. Work in isochoric transformations, reversible isobars, reversible isotherms of an ideal gas. First law of thermodynamics. Internal energy. Free expansion of an ideal gas. Internal energy of an ideal gas. Molar specific heats of an ideal gas. Reversible adiabatic transformations of an ideal gas.
16. Thermal machines, refrigeration machines, heat pumps. Performance and COP. Carnot machine. Second law of thermodynamics, Clausius and Kelvin statements. Entropy. Entropy and disorder.
* Electromagnetism
17. Electrical phenomena, electric charge, charge density. Conductors and insulators. Induction and polarization. Coulomb's law. Electric force and field, superposition principle, field of a point charge. Electric dipole. Electric field lines. Motion of an electron in a uniform electric field. Electric field flux, Gauss theorem. Uniformly charged sphere, infinite flat plate, double layer.
18. Electrostatic potential, electrostatic potential energy. Potential of a point electric charge. Potential difference in a uniform electric field.
19. Conductors in electrostatic equilibrium. Coulomb theorem, point effect. Charged conducting sphere. Electrostatic screen. Electric capacity. Condensers, plane condenser. Energy stored in a capacitor. Energy density of the electric field. Dielectric filled capacitor.
20. Direct electric current, drift velocity, current density. Electric resistance, Ohm's laws. Joule effect.
21. Magnetic phenomena, magnetic field. Force on a wire carrying a current in an external magnetic field. Lorentz force. Motion of a charge in a uniform magnetic field with velocity perpendicular to the field. Speed selector and mass spectrometer. Magnetic field generated by a current-carrying wire. Biot-Savart law. Magnetic field generated by a circular coil (in the center) carrying current. Gauss's theorem for the magnetic field. Faraday's law. Lenz's law.
Prerequisites
Basic mathematics common to all five-year upper secondary school courses.
The following topics will be re-covered in class: equivalences, proportions, powers, logarithms, exponential function, sine and cosine, elements of trigonometry, various grades equations, inequalities, systems of linear equations. Elements of vector, differential, integral calculus are included in the course.
Books
Raymond A. Serway e John W. Jewett, Jr.
Fondamenti di Fisica
Raymond A. Serway e John W. Jewett, Jr.
Principi di Fisica, V Edizione
(Ed. EdiSES S.r.l)
Ferrari, Luci, Mariani, Pelissetto
Fisica 1 e Fisica 2, Idelson-Gnocchi, 2013
Focardi,Mass,Uguzzoni
Fisica Generale: Meccanica e termodinamica, Ambrosiana, 2005
Filatrella, Romano
Elaborazione Statistica dei dati sperimentali con elementi di laboratorio
(Ed. EdiSES)
Fowler, Jarvis, Chevannes
Statistica per le professioni sanitarie
(Ed. EdiSES)
Wayne W. Daniel
Biostatistica, concetti di base per l’analisi statistica delle scienze dell’area Medico-Sanitaria
(Ed. EdiSES)
Frequency
The course takes place in presence. Attendance is not mandatory but strongly recommended.
Exam mode
The exam consists of a written and an oral part.
The written part consists of a few problems/exercises that are similar to those discussed during the lessons (typically shorter/simpler), to be solved in 2-3 hours.
The written part score needs to be >=15 to be able to do the oral part.
The oral part consists of a discussion about one or several topics covered by the program. The oral part can be taken in the same session as of the written part or in the next two sessions (excluding extraordinary sessions in April/November).
Taking part in a written exam cancels the previous one, except if the person leaves within the first hour.
No textbooks or notes are allowed during the written part. The use of a formula sheet is allowed. Mobile phones are not allowed, not even as calculator.
Sufficient knowledge of the topics covered by the program is required to pass the exam with minimum marks. To achieve
a maximum score of 30/30 cum laude, the student must demonstrate an excellent knowledge of the treated topics, and the ability to expose them in a logical way and with the appropriate scientific language.
Lesson mode
The course is delivered through lectures supplemented by exercises. The exercises, provided throughout the course, cover all the topics covered during the theoretical lessons and prepare students for the written test. Various summary sessions are foreseen in which various representative exercises of those administered in the exams are illustrated. The following are made available on the e-learning platform: a diary of the lessons, handouts, exercises and suggested quiz to integrate what was done in class with the relative solutions.