Semester | Mand. | Option | Filières |
BA6 | x | ||
MA2, MA4 | x |
Lecture | 1 weekly |
Practical work | 2 weekly |
Study plan | Semester | Mand. | Option | Filières |
Computational science and Engineering 2018-19 | MA2 | x | ||
Computational science and Engineering 2018-19 | MA4 | x | ||
Physique 2018-19 | BA6 | x |
Cursus | Sem. | Type |
---|---|---|
Computational science and Engineering | MA2, MA4 | Opt. |
Physics | BA6 | Opt. |
Fourier series and transforms Introduction to the Fourier series and transforms and their application. Mathematical properties: convergence, convolution, correlation, Gibbs phenomenon and the Wiener-Khinchin theorem. Fourier transform on discrete sampled data: aliasing and sampling theorem. Discrete Fourier transform (DFT) and fast Fourier transform (FFT). Applications: spectral analysis, filters. Fourier transforms in higher dimensionality.
Linear systems Introduction and examples. Gauss-Jordan elimination, LU factorization. Iterative refinement: tridiagonal and band diagonal systems. Iterative methods and preconditioning: Jacobi, Richards and gradient methods. Conjugate gradient method. Iterative vs direct methods.
Matrix manipulation and eigenvalues problems Introduction and examples. Properties and decomposition. Poweriteration. QR decomposition and iterative procedure. Singular value decomposition (SVD).
1st and 2nd years numerical physics courses
Ex cathedra presentations, exercises and work under supervision
3 reports during the semester
J. F. James, A Student's guide to Fourier transforms, CUP 2011
L. N. Trefethen and D. Bau III, Numerical linear algebra, SIAM 1997
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Pendant le semestre
During the semester
Session été
Session summer
ETE
ETE
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Pendant le semestre
During the semester
Session été
Session summer
ETE
ETE
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Pendant le semestre
During the semester
Session été
Session summer
ETE
ETE
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