
Course unit
MATHEMATICAL PHYSICS
INP8084118, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary 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 
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 2dim dynamical systems. Biforcations. Autooscillating 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: LagrangeDirichlet theorem, linearization around an equilibrium, normal modes. Introduction to variational methods: functionals, EulerLagrange equation, examples. Hamilton variational principle. 
Planned learning activities and teaching methods:

Frontal lessons, including theory and exercises. 
Textbooks (and optional supplementary readings) 

Steven Strogatz, Nonlinear dynamics and Chaos. : , .

Giancarlo Benettin, Appunti ed Eserciziario per il corso di Fisica Matematica. : , .


