By Gerd Baumann (auth.)
Mathematica for Theoretical Physics:
Classical Mechanics and Nonlinear Dynamics
This moment variation of Baumann's Mathematica® in Theoretical Physics indicates readers how one can remedy actual difficulties and take care of their underlying theoretical ideas whereas utilizing Mathematica® to derive numeric and symbolic recommendations. each one instance and calculation will be evaluated via the reader, and the reader can switch the instance calculations and undertake the given code to comparable or related difficulties.
The moment version has been thoroughly revised and elevated into volumes:
The first quantity covers classical mechanics and nonlinear dynamics. either themes are the root of a customary mechanics direction. the second one quantity covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus.
New examples were additional and the illustration has been transformed to supply a extra interactive problem-solving presentation. This booklet can be utilized as a textbook or as a reference paintings, through scholars and researchers alike. a quick thesaurus of phrases and features is inside the appendices.
The examples given within the textual content is also interactively used and altered for the reader’s purposes.
The writer, Gerd Baumann, is affiliated with the Mathematical Physics department of the collage 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 usually hosts seminars and lectures on symbolic computing on the collage of Ulm and at TECHNISCHE UNIVERSITÄT MÜNCHEN (TUM), Munich.
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Extra resources for Mathematica® for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics Volume 1
Example text
Finally, the x3 -axis remains unchanged: ij 0 yz j z x3 = jjj 0 zzz; j z k1{ 2. x3 0 jij zyz jj 0 zz jj zz j z k1{ The following transformation: illustration demonstrates this kind of coordinate Another transformation about the x1 -axis is defined as follows: 0 0y ij 1 zz j 0 1 zzz lx1 = jjj 0 j z k 0 -1 0 { ij 1 0 0 yz jj z jj 0 0 1 zzz jj zz k 0 -1 0 { In the next step, let us apply the two rotations about the x3 - and the x1 -axis in such a way that we first carry out the rotation around the x3 -axis followed by a rotation about the x1 -axis.
The transposition of a matrix A is denoted by AT . IdentityMatrix@3D ij l11 l21 l31 jj jj l12 l22 l32 jj k l13 l23 l33 yz zz zz zz { Consider matrix l to be known. l = 1. 17) if detHlL 0. Note that in numerical work it sometimes happens that detHlL is almost equal to 0. Then, there is trouble ahead. In Mathematica, the inverse of a matrix is calculated by the function Inverse[]. The application of this function to the matrix l gives us 2. l -1 D ij 1 0 0 yz jj z jj 0 1 0 zzz jj zz k0 0 1{ which, in fact, reproduces the identity matrix.
By solving the following mathematical conjecture, we simultaneously demonstrate the creation of an interactive function in Mathematica. 1) under the initial conditions f0 = cosHxL and f1 = sinHxL results in a polynomial whose coefficients are given by trigonometric functions. The resulting polynomial can be represented in the form ¶ n n f¶ = cosHxL ⁄¶ n=0 an x + sinHxL ⁄n=0 bn x . 2) The related Mathematica representation is located in the variable poly. It reads poly = Cos@xD ‚ a@nD xn + Sin@xD ‚ b@nD xn n=0 n=0 Cos@xD ‚ a@nD xn + Sin@xD ‚ b@nD xn n=0 n=0 The sums in the representation of the polynomial extend across the range 0 < n < ¶.