MATHEMATICAL AND NUMERICAL METHODS
Corso
A Padova
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Descrizione
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Tipologia
Corso
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Luogo
Padova
Written report on the exercises done during the classes. Oral exam based on the written report and on the topics of the course.
Sedi e date
Luogo
Inizio del corso
Inizio del corso
Opinioni
Programma
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.
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Ti aiuterà a confrontare vari corsi e trovare l'offerta formativa più conveniente.
MATHEMATICAL AND NUMERICAL METHODS