First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
ASTROPHYSICS AND COSMOLOGY
Course unit
MATHEMATICAL AND NUMERICAL METHODS
SCP9086342, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
ASTROPHYSICS AND COSMOLOGY
SC2490, Degree course structure A.Y. 2019/20, A.Y. 2019/20
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Degree course track Common track
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL AND NUMERICAL METHODS
Website of the academic structure http://astrophysicsandcosmology.scienze.unipd.it/2019/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 MICHELA MAPELLI FIS/05

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2019 course timetable

Syllabus
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: Gauss-Seidel 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, Runge-Kutta scheme, Hermite scheme); example: the astrophysical N-body 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 CS-R9525.
* Guido van Rossum: Python Tutorial. May 1995. CWI Report CS-R9526.
* Lecture notes
* Numerical Methods in Engineering with Python, Jaan Kiusalaas, Cambridge University Press, ISBN-13: 978-1107033856, ISBN-10: 1107033853
* Numerical Recipes in C, W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Cambridge University Press, ISBN-13: 978-0521431088, ISBN-10: 0521431085
* Computational Physics, Mark Newman, Amazon Digital Services, ISBN-13: 978-1480145511, ISBN-10: 1480145513
Textbooks (and optional supplementary readings)
  • Mark Newman, Computational Physics. --: Amazon Digital Services, --. ISBN-10: 1480145513, ISBN-13: 978-1480145511

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