# A Crash Course in Mathematica by Stephan Kaufmann By Stephan Kaufmann

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

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Look at the two following definitions: In:= OUI= In:= myExpandl [x_l =Expand [ (1 + x) A 21 1 +2 x +x2 myExpand2 [x_l : = Expand [ (1 + x) A 21 50 Part 1 When applied to a single symbol or a number they give the same result. In[78):= Out[78)= In[79):= Out[79)= myExpandl [a] 1 + 2 a + a2 myExpand2 [a] 1 + 2 a + a2 But if we evaluate them for a sum, this sum is simply substituted for x in the first version. In[80):= Out[80)= myExpandl [a + b] 1 + 2 (a + b) + (a + b) 2 On the other hand, with a delayed definition the sum is substituted and the Expand of the resulting expression is then calculated.

We substitute the solution for x into the equation with: In[90):= Out[90)= myEquation /. firstSolution True The answer to the frequently asked question, how to set x to this value definitively, is: In[9t):= Out[91)= In[92):= Out[92)= x =x /. firstSolution -1 + b a x +1 -1 + b 1 - --a- or in one step: 53 The Basics In:= x =x == 1, /. Solve [a x + b General: :ivar : - -1 +b a xl  is not a valid variable. ReplaceAll: : reps : {True} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.

In:= Expand [ (a + b) "2/ (c + d) "2] Out= In:= (a + b) 2 ExpandAll [ - - - (c + d) 2 ~ Out= 2ab ~ c2 + 2 cd + d 2 + c 2 + 2 cd + d 2 + c 2 + 2 cd + d 2 To avoid conflicts between names of built-in Mathematica functions and other objects, you should begin your own names with a small letter. In:= myFunction Out= myFunction In:= x Out= x Spaces L) can be used as long as they do not change the meaning of expressions. ) • Parentheses, Brackets, and Braces Arguments of Mathematica functions are placed in square brackets and separated by commas.