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Introduction to numerical analysis and scientific computing with python

Course Type: 
PhD Course
Master Course
Academic Year: 
30 h

Practical Information on the course 

This is a Joint course, between SISSA PhD in Mathematical Analysis, Modeling, and Applications, Theoretical and Scientific Data Science, and the Master in High Performance Computing

It shows the basics of numerical analysis with both frontal lectures and python laboratories

The lectures are in the MHPC room in Via Beirut 2--4

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Syllabus 2022-2023

  • Vector spaces, vector norms, matrices, and matrix norms
  • Basic linear algebra: direct solution of linear systems
  • Not so basic linear algebra: iterative solution of linear systems
  • Polynomial interpolation
  • Interpolatory Quadrature rules
  • L2 projection
  • Least square approximation
  • Finite Difference Methods - 1d Poisson PDE
  • Finite Difference Methods - 2d and 3d Poisson PDE
Python laboratories

  • Introduction to Python
  • Numpy, Scipy, Vectors, Matrices, and their norms
  • Implementation of Gauss elimination, comparison with scipy
  • Implementation of Richardson, gradient, and conjugate gradient, comparison with scipy
  • Using numpy for polynomial approximation
  • Using numpy for numerical integration
  • Putting things together: mass matrices, least square matrices, L2 projection
  • Solving a simple PDE in 1d with finite differences
  • Solving a simple PDE in 2d/3d with finite differences
References and Text Books:
  • A. Quarteroni, R. Sacco, and F. Saleri. Numerical mathematics, volume 37 of Texts in Applied Mathe- matics. Springer-Verlag, New York, 2000. 
    [E-Book-ITA] [E-Book-ENG]
  • A. Quarteroni. Modellistica Numerica per problemi differenziali. Springer, 2008. 
  • A. Quarteroni. Numerical Models for Differential Problems. Springer, 2009. 
  • A. Quarteroni and A. Valli. Numerical approximation of partial differential equations. Springer Verlag, 2008. 
  • S. Brenner and L. Scott. The mathematical theory of finite element methods. Springer Verlag, 2008.
  • D. Boffi, F. Brezzi, L. Demkowicz, R. Durán, R. Falk, and M. Fortin. Mixed finite elements, compatibility conditions, and applications. Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 26–July 1, 2006. Springer Verlag, 2008.
  • D. Arnold. A concise introduction to numerical analysis. Institute for Mathematics and its Applications, Minneapolis, 2001. 
  • A. Quarteroni, F. Saleri, P. Gervasio. Scientific Computing with Matlab and Octave. Springer Verlag, 2006.   
  • B. Gustaffson Fundamentals of Scientific Computing, Springer, 2011
  • Tveito, A., Langtangen, H.P., Nielsen, B.F., Cai, X. Elements of Scientific Computing, Springer, 2010

Note that, when connecting from SISSA, all of the text books above are available in full text as pdf files.

Next Lectures: 

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