First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
ASTRONOMY
Course unit
MATHEMATICAL PHYSICS
SCN1032593, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
ASTRONOMY
SC1173, Degree course structure A.Y. 2010/11, A.Y. 2017/18
N0
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Degree course track ASTRONOMIA [001PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL PHYSICS
Website of the academic structure http://astronomia.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Physics and Astronomy
Mandatory attendance
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 MASSIMILIANO GUZZO MAT/07

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
INP5070521 DYNAMICAL SYSTEMS (MOD. B) MASSIMILIANO GUZZO IN2191

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/07 Mathematical Physics 5.0
Other -- -- 1.0

Mode of delivery (when and how)
Period Second semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Lecture 6.0 48 102.0 No turn

Calendar
Start of activities 26/02/2018
End of activities 01/06/2018

Examination board
Examination board not defined

Syllabus
Prerequisites: Linear algebra and calculus with functions of several variables.
Target skills and knowledge: This course provides an introduction to the study of the ordinary and partial differential equations with the modern point of view of
dynamical systems. Examples from Astronomy and from Physics will
be considered.
Examination methods: Written examination
Assessment criteria: Evaluation of the written examination.
Course unit contents: 1. Ordinary differential equations: Cauchy theorem, phase-space flow, dependence on the initial conditions; linear equations; phase-portraits, first integrals; equilibrium points; linearizations, stable, center and unstable spaces.

2. Integrable systems: elementary examples from population dynamics, from Mechanics and from Astronomy; integrability of mechanical systems, action-angle variables, examples.

3. Non-integrable Systems: discrete dynamical systems, Poincare' sections; bifurcations, elementary examples. Stable and Unstable manifols, homoclinic chaos; Lyapunov exponents, the forced pendulum and other examples; Center manifolds and partial hyperbolicity. The three body-problem, the Lagrange equilibria,
Laypunov orbits, the tube manifolds.

THE FOLLOWING TOPICS (4) AND (5) ARE ONLY IN THE PART FOR THE STUDENTS OF THE SECOND CYCLE DEGREE IN ASTRONOMY

4. Linear PDEs of first and second order, well-posed problems,
the vibrating string, 1-dimensional wave equation, normal modes of vibrations, heat equation, Fourier series, 2-dimensional wave equation, Laplace operator and polar coordinates, separation of variables, Bessel functions, eigenfunctions of the Laplacian operator.

5. Laplace operator and spherical coordinates, separation of variables, Legendre polynomials and associate functions, Spherical harmonics, multipole expansions, L2 operator-eigenvalues and eigenfunctions, complete solution of the wave equation in space, Schrodinger polynomials.

THE FOLLOWING TOPICS (6) ARE ONLY IN THE PART FOR THE STUDENTS OF THE SECOND CYCLE DEGREE IN MATHEMATICAL ENGINEERING

6. Examples and Applications: examples of analysis of three and four dimensional systems; limit cycles; the Lorenz system, the three-body problem; examples from fluid dynamics, non autonomous dynamical systems, chaos indicators, Lagrangian Coherent Structures.
Planned learning activities and teaching methods: Classroom lectures and exercises.
Additional notes about suggested reading: Lecture notes.
Textbooks (and optional supplementary readings)