文档介绍：THE THIRD BRANCH
OF PHYSICS
Essays on puting
Norbert hofer
June 26, 2005
Copyright c 2005 by Norbert hofer
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Contents
About This Manuscript v
1 Analytic and Numeric Solutions; Chaos 1
2 Themes of Numerical Analysis 4
3 Roundoff and Number Representation 10
4 Programming Tools 16
5 Physics Sampler 21
6 Discrete Approximations of the Continuum 29
7 From Programs to Data Analysis 36
8 Performance Basics 41
9 Bytes at Work 47
10 Counting Operations 52
11 Random Numbers and Stochastic Methods 58
12 Algorithms, Data Structures, plexity 62
13 putation 68
14 A Crash Course on Partial Differential Equations 72
15 Lesson from Density Functionals 79
Answers to Problems 83
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About This Manuscript
Fundamental scientific discoveries have been made with the help -
putational methods and, undoubtedly, more are e. For example,
commonalities (universality) in the behavior of chaotic systems had not
been discovered or understood puters. Only with numerical
computations is it possible predict the mass of the proton so accurately
that fundamental theories of matter can be put to test. And numerics
is not only used to determine the binding between atoms and molecules,
but has also led to new quantum-mechanical methods that revolutionized
chemistry and materials science. Such examples highlight the enormous
role of numerical calculations for basic science.
Many researchers find themselves spending much time puta-
tional work. While they are trained in the theoretical and experimental
methods of their field, comparatively little material is currently available
about putational branch of scientific inquiry. This manuscript
is intended for researchers and students who embark on research involv-
ing putations. It is a collection of concise writings in the
style of summaries, discussions, and lectures. It uses an interdisciplinary
approach, puter technology, numerical methods and their in-
terconnections are treated with the