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| Detailed information |
| Original study plan |
Master's programme Nanoscience and Technology 2020W |
| Objectives |
Introduction to numerical Methods in Physics; solving initial value problems for systems of ordinary differential equations (ODEs); solving boundary- and eigenvalue problems for ODEs with finite differences and finite elements; linear algebra: iterative solution of linear systems and eigenvalue problems; introduction to partial differential equations.
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| Subject |
- Numerical errors, floating-point numbers
- Basic numerical analysis: Interpolation, differentiation, finding roots, quadrature (newton-cotes, Gauss quadrature)
- Solution of initial value problems for systems of ODEs: Euler-, Runge-Kutta-, Predictor-corrector methods, symplectic integrators
- Three-body problem, introduction to classical chaos
- Boundary- and Eigenvalue problems
- Finite difference discretization
- Finite element discretization
- Iterative solution of linear systems (Jacobi, Gauss-Seidel, SOR, Conjugate Gradient methods, preconditioning)
- Iterative solution of eigenvalue problems (Inverse iterations, Rayleigh quotient iterations, subspace iteration method, Lanczos method, generalized eigenvalue problems)
- Introduction partial differential equations
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| Criteria for evaluation |
2 term papers:
- celestial mechanics problem (chaotic motion in the 3-body problem, Lagrange points)
- finite element simulation (Schrödinger equation of a quantum dot)
The grade for the lecture is based on quality and "scientific soundness" of the papers turned in.
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| Language |
English |
| Study material |
Material distributed in class:
- Lecture notes as pdf
- Mathematica Example Notebooks/CDF files
Literature:
- Paul DeVries, "A first course in computational physics", Wiley 1994
- Josef Stör, Roland Bulirsch, "Numerische Mathematik 1" and "Numerische Mathematik 2", Springer (also available in English)
- Gene H. Golub, Charles F. Loan, "Matrix Computations", John Hopkins University Press
- Z. Bai, J. Demmel, J. Dongarra et al, "Templates for the Solution of Algebraic Eigenvalue Problems", SIAM 2000
- R. Barrett, M. Berry, T.F. Chan et al, "Templates for the Solution of Linear Systems", SIAM 200g
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| Changing subject? |
No |
| Earlier variants |
They also cover the requirements of the curriculum (from - to)
TPMPTVOCOP1: VO Computational Physics I (2009W-2016S)
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