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Numerical Recipes in Physics with Mathematica Exercises V. Ossenkopf & M. Röllig

Details

• Summer 2011
  
• 2h lecture, 1h exercises
  
• Exam: numerical solution of a selected physics problem
  

Contents

Introduction

Numerical formulation of physical problems
Basics of Mathematica programming

• rule-based, functional, and procedural

Scaling and complexity

The Turing machine
Recursion
Series expansions
P vs. NP
Optimizing Mathematica code

Interpolation and extrapolation

Polynomials
N dimensions
Physical models for extrapolation
Irregular data

Numerical integration

Tabulated functions
N dimensions
Monte-Carlo methods

• Random numbers
• Distribution functions

Linear equation systems

Eigensystems
Inversion
Sparse arrays
Iterative methods

Nonlinear systems

Root finding

• Convergence
• Completeness

Decomposition
discrete programming

Minimization

Local vs. global
Gradient methods
Randomization, simulated annealing
Genetic algorithms
Nested sampling

Fourier transform

diskretization problems

Differential equations

Discretization schemes
Boundary and starting conditions
Stiff systems
Predictor-corrector methods
Partial differential equations
Solutions in Fourier space

Modelling of data

Error propagation
Least-squares and maximum likelihood
Confidence limits

Addressees

• Students at master level of physics and geophysics
• Can be taken as part of the "Schwerpunkt Astrophysik" or as separate special lecture.

Literature

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P.Flannery

Numerical Recipes in [FORTRAN | C | C++ | Fortran 90]

M.Trott

The Mathematica GuideBook for Numerics

Donald R. Knuth

The Art of Scientific Programming

M.Trott

The Mathematica Guidebook for Programming

M.Trott

The Mathematica Guidebooks for Graphics

M.Trott

The Mathematica Guidebook for Symbolics

Patrick T. Tam

A Physicist's Guide to Mathematica

Wolfram Research

Mathematica Tutorials

M. Röllig

Lecture Notes

R.H. Enns, G.C. McGuire

Nonlinear Physics with Maple for Scientists and Engineers