Advanced Topics in Physics
A.Y. 2022/2023
Learning objectives
Knowledge of physical phenomena and methods, which are compulsory for the study of geophysics: gravitational field; dynamics of rigid bodies; oscillatory systems and wave phenomena; basic theory of electromagnetic fields. The discussion of these topics requires the knowledge of some mathematical concepts (differential operators, partial differential equations and basic methods for their analytical solution), which are introduced during the lectures.
Expected learning outcomes
At the end of the course unit, the students will acquire:
1) Knowledge skills (ability to describe, in correct mathematical and physical terms, the motion of rigid bodies, the gravitational field, the behavior of oscillatory systems and wave phenomena, the propagation of electromagnetic waves; ability to solve problems, referred to these topics);
2) Communication skills (ability of exposing scientific topics, related to basic elements of mechanics and electrodynamics);
3) Learning skills (ability to read scientific papers and books to improve the knowledge on the topics introduced during the lectures).
1) Knowledge skills (ability to describe, in correct mathematical and physical terms, the motion of rigid bodies, the gravitational field, the behavior of oscillatory systems and wave phenomena, the propagation of electromagnetic waves; ability to solve problems, referred to these topics);
2) Communication skills (ability of exposing scientific topics, related to basic elements of mechanics and electrodynamics);
3) Learning skills (ability to read scientific papers and books to improve the knowledge on the topics introduced during the lectures).
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
- Gravitational field: Poisson's and Laplace's equations, spherical harmonics, Dirac's distribution, and concept of point mass.
- Advanced mechanics: rotation of a rigid body and applications.
Waves and oscillations: free oscillations of simple systems (pendulum, spring, LC circuit), normal modes of oscillation, beats; transversal oscillations of a continuous string, wave equation, Fourier's analysis; forced and damped oscillations, resonance; progressive waves, phase velocity, modulation and group velocity; wave energy and intensity; reflection and transmission of waves; superposition principle and interference.
- Electromagnetic waves: Maxwell's equations in vacuum and in matter; Energy, momentum and angular momentum carried by electromagnetic fields; linear and circular polarization; electromagnetic waves in materials of geophysical interest, microscopic model of matter.
The presentation of the above listed topics is supported by recalling some basic concepts of physical-mathematics: definition and physical meaning of differential operators (gradient, divergence, curl, laplacian); Fourier's and Laplace's transforms and their use for the solution of partial differential equations; methods of separation of variables for the solution of wave equations, eigenvalue problem, Green's functions.
- Advanced mechanics: rotation of a rigid body and applications.
Waves and oscillations: free oscillations of simple systems (pendulum, spring, LC circuit), normal modes of oscillation, beats; transversal oscillations of a continuous string, wave equation, Fourier's analysis; forced and damped oscillations, resonance; progressive waves, phase velocity, modulation and group velocity; wave energy and intensity; reflection and transmission of waves; superposition principle and interference.
- Electromagnetic waves: Maxwell's equations in vacuum and in matter; Energy, momentum and angular momentum carried by electromagnetic fields; linear and circular polarization; electromagnetic waves in materials of geophysical interest, microscopic model of matter.
The presentation of the above listed topics is supported by recalling some basic concepts of physical-mathematics: definition and physical meaning of differential operators (gradient, divergence, curl, laplacian); Fourier's and Laplace's transforms and their use for the solution of partial differential equations; methods of separation of variables for the solution of wave equations, eigenvalue problem, Green's functions.
Prerequisites for admission
Basic knowledge of mechanics (kinematics and dynamics of a point body), geometrical optics, electrical and magnetic fields.
Teaching methods
The course units will be organized with frontal lectures (4 cfu, corresponding to 32 hours) and exercises (2 cfu, corresponding to 24 hours). Tutorial activity to support students with a weak basic knowledge of physics and mathematics will be possible and activated, if necessary.
Teaching Resources
Notes supplied by the teacher, available on Ariel.
Suggested textbooks:
a) "Fundamentals of Geophysics", di W. Lowrie, Cambridge University Press
b) "A Student's Guide to Geophysical Equations", W. Lowrie, Cambridge University Press
c) "Geodynamics", D.L. Turcotte & G. Schubert, Cambridge University Press
Suggested textbooks:
a) "Fundamentals of Geophysics", di W. Lowrie, Cambridge University Press
b) "A Student's Guide to Geophysical Equations", W. Lowrie, Cambridge University Press
c) "Geodynamics", D.L. Turcotte & G. Schubert, Cambridge University Press
Assessment methods and Criteria
The examination consists in a written exam, followed by on oral interview.
The written exam consists in the solution, in 2 hours, of 3 or 4 exercises on the topics treated in the lectures. The positive outcome of the written examination is valid for the entire academic year and gives access to the oral interview.
The oral interview starts with the discussion of the written test and covers the entire program of the course.
The final assessment will be based on the following criteria: proper solutions of problems; knowledge of the topics treated during the lectures; critical reasoning; skill in the use of specialist lexicon.
The final score will be expressed in thirtieth.
The written exam consists in the solution, in 2 hours, of 3 or 4 exercises on the topics treated in the lectures. The positive outcome of the written examination is valid for the entire academic year and gives access to the oral interview.
The oral interview starts with the discussion of the written test and covers the entire program of the course.
The final assessment will be based on the following criteria: proper solutions of problems; knowledge of the topics treated during the lectures; critical reasoning; skill in the use of specialist lexicon.
The final score will be expressed in thirtieth.
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/07 - APPLIED 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/07 - APPLIED PHYSICS
Practicals with elements of theory: 24 hours
Lessons: 32 hours
Lessons: 32 hours
Professor:
Piovella Nicola Umberto Cesare
Professor(s)