By Gerd Baumann (auth.)
Mathematica for Theoretical Physics:
Classical Mechanics and Nonlinear Dynamics
This moment variation of Baumann's Mathematica® in Theoretical Physics exhibits readers find out how to remedy actual difficulties and take care of their underlying theoretical techniques whereas utilizing Mathematica® to derive numeric and symbolic recommendations. each one instance and calculation may be evaluated via the reader, and the reader can swap the instance calculations and undertake the given code to comparable or related difficulties.
The moment version has been thoroughly revised and accelerated into volumes:
The first quantity covers classical mechanics and nonlinear dynamics. either themes are the foundation of a typical mechanics path. the second one quantity covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus.
New examples were extra and the illustration has been transformed to supply a extra interactive problem-solving presentation. This ebook can be utilized as a textbook or as a reference paintings, through scholars and researchers alike. a short thesaurus of phrases and services is inside the appendices.
The examples given within the textual content is additionally 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 a variety of invited talks at universities and alike. He on a regular basis 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
1) is executed by the sequence AppendToAlistf, 2 i listfP2T y listfP1T IntegrateAj cccccccc z z , xEE êê Simplify j cccccccccccccccc k listfP1T { 8Cos@xD, Sin@xD, x Cos@xD + Sin@xD< in which we append the result from an integration of the iteration formula to listf by means of the function AppendTo[]. The next step just changes the indices of the iteration and is given by AppendToAlistf, 2 i listfP3T z y listfP2T IntegrateAj cccccccc z , xEE êê Simplify j cccccccccccccccc k listfP2T { 9Cos@xD, Sin@xD, x Cos@xD + Sin@xD, 1 cccc x H3 + x2 + 3 x Cot@xDL Sin@xD= 3 Here, we increase the indices of the list elements in listf by one.
By using graphics primitives like Line[], Disk[], Circle[], and so forth, you can create any two- or three-dimensional objects you can imagine. A simple example to combine lines, disks, squares, and circles for depicting the scattering of a particles on a gold bar follows. 22 1. 6 Programming Mathematica not only is an interactive system but also allows one to generate programs supporting scientific calculations. By solving the following mathematical conjecture, we simultaneously demonstrate the creation of an interactive function in Mathematica.
11) We must now establish rules whereby it is possible to multiply two matrices. Let us take a column matrix for the coordinates. 13) or in Mathematica notation O12 O13 O i j 11 q j O x =j j 21 O22 O23 j j k O31 O32 O33 x1 y i z j z j z j x . 2 Mathematical Tools This relation completely specifies the operation of matrix multiplication for the case of a matrix of three rows and three columns operating on a matrix of three rows and one column. The next step is to generalize this result to matrices of n än order.