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AuthorKaufmann, Stephan. author
TitleMathematica as a Tool [electronic resource] : An introduction with practical examples / by Stephan Kaufmann
ImprintBasel : Birkhรคuser Basel, 1994
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8526-3
Descript IX, 430 p. online resource

SUMMARY

More than ten years ago, I wanted to carry out coordinate transformations for Hamiltonian systems, in order to discuss the stability of certain equilibrium posiยญ tions. Basically, the calculations only involved rational expressions, but they turned out to be extremely complicated, because the third and fourth order terms had to be included. After several months of filling whole blocks of paper with forยญ mulas, I was close to resignation. But, by a lucky incident, I met a colleague who showed me the computer algebra package Reduce. It still required a lot of patience and tricks, but Reduce finally did produce the desired results. After this experience, I wondered, why only a few engineers and scientists were aware of the strengths of such computer algebra programs. The mathematical treatment of scientific problems often leads to calculations which can only be solved "by hand" with a considerable investment of time, while a suitable comยญ puter algebra program produces the solution within a couple of seconds or minยญ utes. Even if a closed symbolic solution is not possible, such programs can often simplify a problem, before the cruder tool of numerical simulations is applied


CONTENT

1. Basics -- 1.1 Getting Started -- 1.2 Help! -- 1.3 Numerical Calculations -- 1.4 Symbolic Calculations -- 1.5 Plots: Different Pendulums -- 1.6 Lists -- 1.7 Graphics Programming -- 1.8 More Selected Tools -- 2. Structure -- 2.1 Expressions -- 2.2 Patterns -- 2.3 Transformation Rules and Definitions -- 2.4 Evaluation and Tools for Programming -- 2.5 Modularity -- 2.6 Strings, Text, Messages -- 3. Programming -- 3.1 Programming Methodologies -- 3.2 Developing Programs -- 3.3 Numerics -- 3.4 Long Calculations: RSA -- References


Mathematics Chemometrics Computer software Physics Computational intelligence Mathematics Mathematical Software Math. Applications in Chemistry Mathematics general Computational Intelligence Theoretical Mathematical and Computational Physics



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