First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
AUTOMATION ENGINEERING
Course unit
MATHEMATICAL PHYSICS
INP8084118, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
AUTOMATION ENGINEERING
IN0527, Degree course structure A.Y. 2008/09, A.Y. 2018/19
N0
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL PHYSICS
Department of reference Department of Information Engineering
E-Learning website https://elearning.dei.unipd.it/course/view.php?idnumber=2018-IN0527-000ZZ-2018-INP8084118-N0
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge OLGA BERNARDI MAT/07

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/07 Mathematical Physics 9.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Lecture 9.0 72 153.0 No turn

Calendar
Start of activities 25/02/2019
End of activities 14/06/2019

Examination board
Board From To Members of the board
1 A.A. 2018/2019 01/10/2018 15/03/2020 BERNARDI OLGA (Presidente)
PONNO ANTONIO (Membro Effettivo)
CARDIN FRANCO (Supplente)

Syllabus
Prerequisites: Mathematical analysis, linear algebra, geometry and physics of the bachelor degree in Engineering.
Target skills and knowledge: It is a basic course in mathematical physics. Students will learn the qualitative analysis of dynamics, the Lagrangian formalism and some basic concepts of the Calculus of Variations. Moreover, students will learn to approach a physical model with the rigorous formalism of mathematics and they will discover the powerful and utility of mathematics in the physical applications.
Examination methods: A written test on the exercises and an oral test on the theory.
Assessment criteria: Check of the acquired knowledge, forming a critical and mathematically rigorous mentality and understanding the link between mathematical structure and physical meaning of subjects.
Course unit contents: Qualitative theory of ordinary differential equations (ODE).

Examples. Equilibria, stability and asymptotic stability. Lyapunov Theorem for the stability of equilibria. Phase portraits. Linearization of equations and classification of equilibria for 2-dim dynamical systems. Biforcations. Auto-oscillating systems: the limit cycle in mechanical oscillators and the Van der Pol equation. Examples of chaotic motions.

Lagrangian mechanics.

Holonomic constraints, free coordinates. Kinetic energy, forces and potential energy. Lagrange equations: deduction, normal form, invariance property. Potentials depending on the velocities, charged particle in a magnetic field. Corservation lawa in Lagrangian mechanics: conservation of energy, reduction, Noether theorem. Equilibria, stability and small oscillations: Lagrange-Dirichlet theorem, linearization around an equilibrium, normal modes. Introduction to variational methods: functionals, Euler-Lagrange equation, examples. Hamilton variational principle.
Planned learning activities and teaching methods: Frontal lessons, including theory and exercises.
Textbooks (and optional supplementary readings)