# Mathematical Modeling and Numerical Methods

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### Mathematical Modeling and Numerical Methods

 Code: 205286 ECTS: 0.0 Lecturers in charge: prof. dr. sc. Nils Paar - Lectures Take exam: Studomat

### 1. komponenta

Lecture typeTotal
Lectures 20
Exercises 10
Description:
The main objective of the course is to acquire competencies in the applications of numerical methods in modeling various physical systems. The first part of the course includes solving problems on computer in order to acquire practical knowledge and skills in the application of the basic numerical methods, and in the final part of the course more advanced problem in theoretical physics will be solved. The goal is to acquire interdisciplinary competencies required for modeling complex systems using numerical methods and computer programming, that can be applied in any area of fundamental or applied sciences.
Course content:
Application of computer programming in the C programming language in solving problems in physics. Numerical accuracy and error analysis. Numerical derivation. Operations with vectors and matrices, solving linear systems of equations. Nonlinear equations and root finding - bisection method, Newton-Raphson method, secant method. Numerical interpolation, extrapolation and fitting to physical data. Numerical integration - Newton-Cotes quadrature, Gaussian quadrature, multidimensional integration in the description of physical systems. Monte-Carlo methods in the description of radioactive decay, Monte-Carlo integration. Numerical simulation of random walk, diffusion, Metropolis algorithm. The eigenvalue problem, diagonalization, Jacobi and Hausholder methods. Differential equations - Euler, Runge-Kutta, Adams methods in describing the dynamics of nonlinear oscillators, and the properties of neutron stars and white dwarfs. The problem of boundary conditions, shooting method in solving the Schroedinger equation using various potentials. Partial differential equations in solving the problem of diffusion. Fourier analysis of nonlinear oscillations. The algorithm of fast Fourier transform and its application to spectral analysis. Methods of parallelization on a cluster and grid computing systems and applications in modeling physical systems.
Literature:
1. Morten Hjorth Jensen, Computational Physics, University of Oslo, 2009.
2. S.E. Koonin, D.C. Meredith: Computational Physics, Addison-Wesley, 1990.
3. Rubin H. Landau, Manuel Jose Paez, Cristian C. Bordeianu, A Survey of Computational Physics - Introductory Computational Science, Princeton University Press, 2008.
4. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery: Numerical Recipes, The Art of Scientific Computing, Cambridge University Press, 2002.
 1. semester Nuklearna fizika - izborni predmeti - Mandatory smjer - Nuclear physics
Consultations schedule:

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