# Coursebooks

## Computational physics III

Yazyev Oleg

English

#### Withdrawal

It is not allowed to withdraw from this subject after the registration deadline.

#### Summary

This course teaches the students practical skills needed for solving modern physics problems by means of computation. A number of examples illustrate the utility of numerical computations in various domains of physics.

#### Content

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).

#### Learning Prerequisites

##### Recommended courses

1st and 2nd years numerical physics courses

#### Learning Outcomes

By the end of the course, the student must be able to:
• Choose the most suitable algorithm for solving given problem
• Integrate algorithms in computer codes and evaluate their performance
• Solve actual physics problems using numerical tools

#### Teaching methods

Ex cathedra presentations, exercises and work under supervision

#### Assessment methods

3 reports during the semester

#### Resources

##### Bibliography

J. F. James, A Student's guide to Fourier transforms, CUP 2011

L. N. Trefethen and D. Bau III, Numerical linear algebra, SIAM 1997

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German