
Course unit
MATHEMATICAL AND NUMERICAL METHODS
SCP9086342, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Other 
FIS/02 
Theoretical Physics, Mathematical Models and Methods 
1.0 
Core courses 
FIS/02 
Theoretical Physics, Mathematical Models and Methods 
5.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
1 Commissione Mathmatical and Numerical Methods 
01/10/2019 
30/11/2020 
MAPELLI
MICHELA
(Presidente)
BOTTACINI
EUGENIO ALESSIO
(Membro Effettivo)
PASQUATO
MARIO
(Supplente)

Prerequisites:

Basics of Mathematical Analysis I, Linear Algebra and Geometry. Basics of Kinematics and Dynamics (General Physics I). 
Target skills and knowledge:

The student will learn how to solve (astro)physical problems numerically. 
Examination methods:

Written report on the exercises done during the classes. Oral exam based on the written report and on the topics of the course. 
Assessment criteria:

The student will learn the main numerical techniques discussed during the lectures. The student will solve the proposed exercises and will learn how to solve an (astro)physical problem with one of the proposed numerical techniques. 
Course unit contents:

Each lecture will consist in a part of theory and a part of exercises.
1. Summary of python programming notions with exercises.
2. Sorting algorithms (selection sort, bubble sort); application of these methods to a physical set of data.
3. Random numbers (random generators, uniform deviates, inversion method, rejection methods); examples of random generation of astrophysical distributions (e.g. Maxwellian distribution of velocities).
4. Solution of linear algebraic equations (direct and indirect methods; example: GaussSeidel method).
5. Interpolation and extrapolation (polynomial, cubic spline); application to an astrophysical sample (e.g. stellar isochrones).
6. Root Finding (bisection method, Newton Raphson method) and exercises.
7. Integration of functions (Monte Carlo method, trapezium method, Romberg integration).
8. Integration of ordinary differential equations (Euler scheme, Leapfrog scheme, RungeKutta scheme, Hermite scheme); example: the astrophysical Nbody problem.
9. Partial differential equations with finite difference methods.
10. Fast Fourier transform (FFT); examples of FFT in astrophysics.
11. Notions of machine learning in astrophysics. 
Planned learning activities and teaching methods:

Each lecture will consist in a part of theory and a part of exercises. 
Additional notes about suggested reading:

* Guido van Rossum: Python Reference Manual. May 1995. CWI Report CSR9525.
* Guido van Rossum: Python Tutorial. May 1995. CWI Report CSR9526.
* Lecture notes
* Numerical Methods in Engineering with Python, Jaan Kiusalaas, Cambridge University Press, ISBN13: 9781107033856, ISBN10: 1107033853
* Numerical Recipes in C, W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Cambridge University Press, ISBN13: 9780521431088, ISBN10: 0521431085
* Computational Physics, Mark Newman, Amazon Digital Services, ISBN13: 9781480145511, ISBN10: 1480145513 
Textbooks (and optional supplementary readings) 

Mark Newman, Computational Physics. : Amazon Digital Services, . ISBN10: 1480145513, ISBN13: 9781480145511

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Interactive lecturing
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex
 Python programming

