Introduction to Mathematica for Physicists (Graduate Texts by Andrey Grozin

By Andrey Grozin

Mathematica is the main customary process for doing mathematical calculations through desktop, together with symbolic and numeric calculations and images. it's utilized in physics and different branches of technological know-how, in arithmetic, schooling and lots of different components. Many vital ends up in physics may by no means be bought with no huge use of computing device algebra. This e-book describes rules of machine algebra and the language of the Mathematica process. It additionally encompasses a variety of examples, in most cases from physics, additionally from arithmetic and chemistry. After analyzing this e-book and fixing difficulties in it, the reader can be capable of use Mathematica successfully for fixing his/her personal difficulties.

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1007/978-3-319-00894-3 4, © Springer International Publishing Switzerland 2014 27 28 4 Patterns and Substitutions And this one—when the argument is a list. By the way, note what happens when a list is being squared. In[8] := { f [{x, y}], f [x + y]}/. f [x List]−>x∧ 2 Out[8] = x2 , y2 , f [x + y] One more example. In[9] := a √ = Sqrt[x]/Sqrt[y] x Out[9] = √ y In[10] := a/. {Sqrt[x]−>u, Sqrt[y]−>v} u Out[10] = √ y Why hasn’t the second substitution triggered? In[11] := FullForm[a] Out[11]//FullForm = Times[Power[x, Rational[1, 2]], Power[y, Rational[−1, 2]]] a does not contain y1/2 , only y−1/2 ; therefore, the substitution y1/2 → v does not work.

X + m . ∗ y−> f [n, m] Out[54] = 2 + x + z And here is our method which always works. In[55] := a = {x + y + z + 2, 2 ∗ x + y + z + 2, 2 ∗ x + 3 ∗ y + z + 2, 2 ∗ x − y + z + 2, x + z + 2, z + 2} Out[55] = {2 + x + y + z, 2 + 2x + y + z, 2 + 2x + 3y + z, 2 + 2x − y + z, 2 + x + z, 2 + z} In[56] := s = {l . ∗ x + f [n , m ]−> f [n + l, m], l . ∗ y + f [n , m ]−> f [n, m + l]} Out[56] = { f [n , m ] + x l . → f [l + n, m], f [n , m ] + y l . → f [n, l + m]} In[57] := a + f [0, 0]//. 5 Conditions Substitutions which apply only when an arbitrary variable satisfies some condition are often needed.

The function Parallelize tries to calculate its argument faster by starting several Mathematica kernels and ordering them to calculate parts of the expression and then collecting these parts together. In[82] := Parallelize[Table[$KernelID, {n, 0, 7}]] Out[82] = {4, 4, 3, 3, 2, 2, 1, 1} ($KernelID is the number of the kernel in which a particular list element has been evaluated). In addition to Table, it can handle Map[ f , {. }] (or f [{. }] where f is a Listable function) and some other cases.

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