Mathematica® for Theoretical Physics: Classical Mechanics - download pdf or read online

By Gerd Baumann (auth.)

ISBN-10: 0387016740

ISBN-13: 9780387016740

ISBN-10: 038725112X

ISBN-13: 9780387251127

ISBN-10: 0387251138

ISBN-13: 9780387251134

Mathematica for Theoretical Physics:
Classical Mechanics and Nonlinear Dynamics
This moment variation of Baumann's Mathematica® in Theoretical Physics exhibits readers easy methods to clear up actual difficulties and take care of their underlying theoretical ideas whereas utilizing Mathematica® to derive numeric and symbolic recommendations. each one instance and calculation should be evaluated through the reader, and the reader can switch the instance calculations and undertake the given code to similar or related difficulties.
The moment variation has been thoroughly revised and elevated into volumes:
The first quantity covers classical mechanics and nonlinear dynamics. either themes are the foundation of a typical mechanics direction. the second one quantity covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus.
New examples were further and the illustration has been remodeled to supply a extra interactive problem-solving presentation. This publication can be utilized as a textbook or as a reference paintings, via scholars and researchers alike. a short thesaurus of phrases and capabilities is inside the appendices.
The examples given within the textual content can be interactively used and altered for the reader’s purposes.
The writer, Gerd Baumann, is affiliated with the Mathematical Physics department of the college of Ulm, Germany, the place he's professor. he's the writer of Symmetry research of Differential Equations with Mathematica®. Dr. Baumann has given quite a few invited talks at universities and alike. He usually hosts seminars and lectures on symbolic computing on the college of Ulm and at TECHNISCHE UNIVERSITÄT MÜNCHEN (TUM), Munich.

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Additional resources for Mathematica® for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics Volume 1

Example text

This function allows you to plot a list of data. The input here is created by means of the function Table[]. The dataset, x which we will represent by ListPlot[] consists of pairs 8x, sinHxL e- ÅÅÅÅ4 < in the range x œ @0, 6 pD. The data are located in the variable tab1. The graphical representation of these pairs of data is achieved by the function ListPlot[] using the dataset tab1 as first argument. All other arguments are used to set temporary options for the function. 2 If you need to represent several sets of data in the same figure, you can use the function MultipleListPlot[] contained in the standard package Graphics`MultipleListPlot`.

However, with Iterate[], we can change the mathematical conjecture in the following way. Let us examine what happens if we use as initial conditions 28 1. Introduction hyperbolic functions instead of trigonometric functions. The result is easy to derive if we use Iterate[] in the form of Iterate[{Cosh[x],Sinh[x]},3] x6 x4 2 x5 : ÅÅÅÅÅÅÅÅÅ + ÅÅÅÅÅÅÅÅ - x2 + x + 1, x - ÅÅÅÅÅÅÅÅÅÅÅÅÅÅ > 45 3 15 Again, we obtain a polynomial whose coefficients are given by hyperbolic functions. The interchange of initial conditions demonstrates that the iteration Iterate@8Sinh@xD, Cosh@xD<, 3D x6 x4 2 x5 : ÅÅÅÅÅÅÅÅÅ + ÅÅÅÅÅÅÅÅ - x2 + x + 1, x - ÅÅÅÅÅÅÅÅÅÅÅÅÅÅ > 45 3 15 provides the same result.

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Mathematica® for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics Volume 1 by Gerd Baumann (auth.)

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