Download A Crash Course in Mathematica by Stephan Kaufmann PDF

By Stephan Kaufmann

"A Crash direction in Mathematica" is a compact creation to this system Mathematica, that's popular in arithmetic, in addition to within the usual and engineering sciences.

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The % sign is used to reference the last output. In[44]:= Expand [%] Out[44]= a 10 + 10 a 9 b + 45 a 8 b 2 + 120 a 7 b 3 + 210 a 6 b 4 + 252 as b S + 210 a 4 b 6 + 120 a 3 b 7 + 45 a 2 b 8 + 10 a b 9 + b 10 Or we make a copy of (a +b) 1 0, select it, and use the palette BasicCalculations > Algebra > Polynomial Manipulations to click Expand [_] into the notebook. The placeholder _ will automatically be replaced by the selection. A In[45]:= Expand[(a+b) "10] Out[45]= a 10 + 10 a 9 b + 45 a 8 b 2 + 120 a 7 b 3 + 210 a 6 b 4 + 252 as b S + 210 a 4 b 6 + 120 a 3 b 7 + 45 a 2 b 8 + 10 a b 9 + b 10 As an alternative we can also select the formula and apply the function Expand [_] from the palette AlgebraicManipulation.

This gives us for example: In[132]:= Out[132]= 121r (a - a Cos [t]) 3 a 2 If 2 clIt Part 1 62 Integrals of expressions with elementary functions are-unlike their derivatives-often no longer elementary. Either the results are special functions that are basically defined as being the integral of another function In[133]:= Out[133]= f Exp [X2 ] ; dlx -{iT Erfi [x] or the integral is returned unevaluated: In[134]:= 12 Exp [x2] Log [x2] Sin [x2] dlx Mathematica does not calculate integrals in the same way you learned in school.

In[102]:= Out[102]= Eliminate [{x - y == d, x + y == s}, x] d == s - 2 Y • Numerical Solutions of Polynomial Equations The solutions of polynomial equations of degree > 4 can generally not be written as rational expressions with radicals. In[103]:= Out[103]= Solve[x5 - x 2 + 1 == 0, x] {{ x ~ Ro 0 t [1 - # 1 2 + # 1 5 &, 1]}, {x~Root[1-#12 +#1 5 &, 2]}, {x~Root[1-#12 +#1 5 &, 3]}, {x~Root[1-#12 +#1 5 &, 4]}, {x~Root[1-#12 +#1 5 &, 5]}} We do not want to get further into Root objects (with which you can also calculate), rather we want to create a numerical approximation of the solutions.

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