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Sometimes I want to ask mathematica to plot or calculate something without given a certain value for it ..

For example I may want to ask mathematica to integrate $\int{a x} \mathrm{d}x$! How to tell him that $a$ is a constant?

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up vote 9 down vote accepted

If you don't specify any information about $a$, Mathematica automatically treats it as a constant, this is the default behaviour. For example, if you input "Integrate[$a$ $x$,$x$]", the output will be $a x^2/2$ as expected. Do not forget that in Mathematica, multiplication is a space, so you need to put a space between $a$ and $x$ for the command I gave to work (otherwise it will treat $ax$ as a single variable).

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The previous answers provide enough context I believe. It is sometimes also useful to give mathematica information about the type of constants (if it's a real or imaginary number for example). This can be done using the option Assumptions. E.g. Integrate[Exp[a x],{x,0,Infinity},Assumptions->{a<0}]

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Shortest through an example:

Dt[a x^2 + b, x, Constants -> {a}]

lets mathematica know that a is a constant here.

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The define operator:

Out[9]= 7
Out[10]= \[Infinity]
Out[12]= 7.
Out[13]= MachinePrecision

Note that the decimal makes the number a literal while just the number is "infinitely" (symbolically) precise.

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I don't want to give mathematica a value for $a$ .. Just to tell it that it is a constant – Osama Gamal Jun 27 '11 at 21:22

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