- Luca Heltai ([email protected])
- Gianluigi Rozza ([email protected])
- Michele Girfoglio ([email protected])
- Marco Feder ([email protected])
Tuesday 22/11 – Aula 004 Thursday 24/11 – Aula 005 Tuesday 29/11 – Aula 128-129 Thursday 01/12 – Aula 128-129 Tuesday 06/12 – Aula 004 Tuesday 13/12 – Aula 128-129 Thursday 15/12 – Aula 128-129 Tuesday 20/12 – Aula 128-129 Thursday 22/12 – Aula 128-129 Tuesday 10/01 – Aula 128-129 Thursday 12/01 – Aula 128-129
This is a Joint course, between SISSA PhD in Mathematical Analysis, Modeling, and Applications, Laurea Magistrale in Matematica, and Laurea Magistrale in Data Science and Scientific Computing.
Most lectures will take place live in room 128-129.
To follow the courses remotely on Zoom:
https://sissa-it.zoom.us/j/85796873697?pwd=cm5HNGRidndvU05UTVAvRkdOdnNrdz09
Meeting ID: 857 9687 3697 Passcode: NumAna
The first lecture will be on the 4th of October 2022 at 14.00 in Room A-128/A-129 and on teams.
If you intend to follow the course, please join the course team:
Recordings for lectures of 2021-2022
Recordings for lectures of 2020-2021
All course material is available at
https://github.com/luca-heltai/numerical-analysis-2022-2023 (this github repository)
In order to access recordings of the lectures, you need to be registered as a Team user at the university of Trieste.
Interested students should send a request to [email protected], indicating that they are Sissa students, taking Prof. Heltai's course and need credentials to access Teams, accompanied by the following information:
- first and last name
- place and date of birth
- tax code
- address of residence or domicile in Italy
- scanned copy of valid front/back ID document
Four Modules of 12h each (1.5 CFU for each module), for a total of 48h, 6 CFU
- Well posedness, condition numbers
- Polynomial based approximations
- Power basis interpolation,
- Lagrange interpolation
- Weierstrass approximation theorem)
- Interpolatory Quadrature rules
- Orthogonal polynomials and Gauss Quadrature Formulas
- L2 projection
- Review of elementary PDEs
- Introduction to Finite Difference Methods
- Introduction to Finite Element Methods
- Least square methods
- Solution methods for Linear Systems
- direct solvers
- iterative solvers
- Eigenvalues/Eigenvectors
- Solution methods for non-Linear systems
- Review of ODEs
- Data assimilation in biomechanics, statistics, medicine, - electric signals
- Model order reduction of matrices
- Linear models for hydraulics, networks, logistics
- State equations (real gases), applied mechanics systems, - grow population models, financial problems
- Applications of ODEs
- example in electric phenomena, signals and dynamics of - populations (Lotke-Volterra)
- Models for prey-predator, population dynamics, automatic - controls
- Applications of PDEs, the poisson problem
- Elastic rope
- Bar under traction
- Heat conductivity
- Maxwell equation
- Introduction to Python, Numpy, Scipy
- Working with numpy arrays, matrices and nd-arrays
- Exercises on Condition numbers, interpolation, quadratures
- Using numpy for polynomial approximation
- Using numpy for numerical integration
- Using numpy/scipy for ODEs
- Solving non-linear systems of equations
- Using numpy/scipy for simple PDEs
Application of the Finite Element Method / Finite Difference Method to the solution of models taken from the course
Further material provided during lectures by Prof. Gianluigi Rozza [https://people.sissa.it/~grozza/amnasc/]
- 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. [E-Book-ITA]
- A. Quarteroni. Numerical Models for Differential Problems. Springer, 2009. [E-Book-ENG]
- A. Quarteroni and A. Valli. Numerical approximation of partial differential equations. Springer Verlag, 2008. [E-Book-ENG]
- S. Brenner and L. Scott. The mathematical theory of finite element methods. Springer Verlag, 2008. [E-Book-ENG]
- 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. [E-Book-ENG]
- D. Arnold. A concise introduction to numerical analysis. Institute for Mathematics and its Applications, Minneapolis, 2001. [E-Book-ENG]
- A. Quarteroni, F. Saleri, P. Gervasio.* Scientific Computing with Matlab and Octave*. Springer Verlag, 2006. [E-Book-ENG]
- B. Gustaffson* Fundamentals of Scientific Computing, *Springer, 2011 [E-Book-ENG]
- Tveito, A., Langtangen, H.P., Nielsen, B.F., Cai, X. *Elements of Scientific Computing, *Springer, 2010 [E-Book-ENG]
Note that, when connecting from SISSA, all of the text books above are available in full text as pdf files.
Instructions for git aware students (and MHPC students)
This repository contains, assignements, workspaces, and other material for the course P1.4
New material will be uploaded frequently,
Remember to set a second remote, either to our private seed
git remote add P1.4_seed https://github.com/luca-heltai/numerical-analysis-2021-2022.git
or (if using ssh keys in your github account)
git remote add P1.4_seed [email protected]:luca-heltai/numerical-analysis-2020-2021.git
and to update before the lectures:
git pull P1.4_seed master
Please consider contributing pull requests to correct typos, or better document the material in this repository!
The content of this repository is distributed with a Creative Common licence. See the file LICENCE.md in this directory for more information.
Some of the material in this repository was adapted from the python-lectures by Robert Johansson. Take a look at his repository for additional material and lectures.