By Stephan Kaufmann

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

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**Example text**

When visualizing mathematical functions and mappings it is important to consider the dimensions of the domain and of the range. This immediately leads to the appropriate Mathematica function. The palette BasicCalculations > Graphics contains templates for the common cases. We start by plotting graphs of functions R ~ R. First we create the graph of the function x ~ sin(x) over a period using Plot. 5 -1 Out[1]= - Graphics - Since we are mainly interested in the graphics themselves, we will suppress the output cells using a semicolon.

The name x can therefore no longer be used as a variable. It is better if we delete the definition for now In[94]:= x =• and avoid the definition for x: In[95]:= Out[95]= x / • Solve [a x + b == 1, xl [1] -1 + b a Nonlinear equations are more interesting: In[96]:= Out[96]= threeSolutions = Solve [XA 3 + X {{X-7- 31 - {X-7- 31 + {X-7- 31 + 4 3 (19_3-[33)113 2 (1+1-)3) 3 (19_3-[33)113 2 (1 - 1-)3) 3 (19_3-[33)113 A2 - x +1 == 0, xl -[33 113 }, -3 (19-333) 1 1 (1-1-)3) (19-3 6 + - -[33 113 33) }, 1 -[33 (1 + I -)3) (19-333) 6 + - 113 }} This gives us three solutions.

In Part 2 we will see many further examples with graphic functions. • Derivatives We have already seen the function D for the calculation of derivatives. Because it is used often, its name is (like N) one of the few exceptions in naming where only a letter is used in place of a whole word. In InputForm the expression to be derived comes first, then the variable or a list containing the variable and the multiplicity of the derivative. 2} Sin [x] -Sin [xl Let us calculate the derivative of an unknown function.