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Introduction to Numerical Analysis & Scientific Computing

Luca Heltai, Gianluigi Rozza
Course Type: 
PhD Course
Academic Year: 
40 h


This course is also part of the Joint SISSA-ICTP HPC master 

The foundations of Numerical analysis

  • Resolution of linear systems with direct methods
  • Resolution of linear systems with iterative methods
  • Polynomial interpolation and projection
  • Numerical Integration
  • Numerical solutions of ODEs
  • Non-linear equations and systems

Numerical Methods for PDEs

  • Finite Elements
  • Elliptic Problems
  • Parabolic Problems
  • Hyperbolic Problems


Teaching support (slides, reports, notes, links)

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.   

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


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