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Introduction to numerical analysis and scientific computing with python

External Lecturer: 
Stefano Piani
Course Type: 
PhD Course
Master Course
Academic Year: 
11-15 December
30 h

Syllabus 2023-2024

  • Basics on Scientific Computing
  • 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
  • Introduction to Finite Difference Methods
  • Introduction to Finite Element Methods

Python laboratories

  • Iterations, absolute and relative errors
  • 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 ODEs and a simple PDE in 1d and 2d with finite differences
  • Solving simple PDEs finite elements

Refrences and books

Scientific Computing & Numerical Analysis 

  • G. Dahlquist & A. Bjorck, Numerical Methods in Scientific Computing. SIAM, 2008. 
  • A. Quarteroni, R. Sacco, and F. Saleri. Numerical mathematics, Springer-Verlag, 2000. 

Numerical Linear Algebra 

  • G.H. Golub & C.F. Van Loan, Matrix Computations. The Johns Hopkins University Press, third edition, 1996. 
  • Lloyd N. Trefethen and David Bau III. Numerical Linear Algebra. SIAM, 1997. 
For AMMA students: please email if you are interested in the course
SISSA Miramare campus
Next Lectures: 

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