Numerical methods in Python (MAGIC099)
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This course is part of the MAGIC core.
The aim of the course is to present several numerical methods that can be used in different scientific areas and implement them using Python. The course starts from the basic idea of an algorithm and evolves discussing, for instance, numerical methods to compute derivatives and integrals of functions, to solve linear systems, and to integrate ordinary and partial differential equations. Each lecture will have an initial part of theory and a final part of Python demo.
Autumn 2019 (Monday, October 7 to Friday, December 13)
Calculus, linear algebra, ordinary and partial differential equations. Some basic concepts of probability, mechanics and fluid mechanics might be used during the examples.
- how to install Python and basic commands, definition of an algorithm, evaluation of the square root
- root finding algorithms: bisection and more advanced methods
- solutions of linear systems, direct and indirect methods
- derivatives of a function using finite differences, methods of finding the function extremes
- Lagrange polynomials and splines
- integration of single variable functions with rectangles and other methods
- Monte Carlo method to compute multivariable integrals
- solutions of ODEs using Euler and Runge-Kutta methods
- integration of PDEs using finite difference algorithms
- fast Fourier transforms (FFTs) and their use in solving PDEs with periodic boundary conditions
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The exam sheet will ask you to address some numerical questions (usually 3) using Python code. You will then have to produce a PDF file containing the code and its outputs. You can solve the questions by using your preferred Python platofrm/IDE (Jupyter Notebook, PyCharm or simply a Python script), but I suggest you to produce a Jupyter notebook so that it is easier to create the PDF file. The exam mark will be a PASS/FAIL, and the threshold to PASS is 50%. The exam will be released at the beginning o the Autumn semester assessment period, this academic year starting on Monday January 6th 2020. (exam moderator: Dr David Aspero)
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