with the the or without the the

[Tukanja]

Which of these four sentences are grammatically correct?

Gauss law, in vacuum, in integral form reads ∫EdS=Q/ε₀.
Gauss law, in vacuum, in the integral form reads ∫EdS=Q/ε₀.

(E, dS are vectors)
(S - closed area)

Gauss law, in vacuum, in mono-dimensional, differential form reads dEx/dx=ρ/ε₀
Gauss law, in vacuum, in the mono-dimensional, differential form reads dEx/dx=ρ/ε₀

Thanks

[Vega]

I suppose it should be "in the integral form", because equations may be in different form: differential, linear, etc. And inteqral equations itself can be: definite and indefenite. So if there's two form of something you should speify it by using "the".

[Tukanja]

Thanks Xkalibur.

Now it seems to me that there should be the the before the word vacuum as well.

Gauss law, in the vacuum, in the integral form reads ∫∫EdS=Q/ε₀.

What do you think about?

So as to support my opinion I want to remark that the ε₀ on the right side of the equation is an electrostatic vacuum parameter (the permeativity of the vacuum, the dielectric constant for the vacuum in the SI system). (SI ~ Standard International)
The other materials do have another electrostatic constant called the absolute permeativity ε or the relative permeativity εr (ε=εr X εo)

By the way does anyone know where to find letters and mathematical operators and signs which I need for mathematical formulas?
Is there any software program in which I could create the operators by myself which I would like to use.

Also I haven't found the words permeativity and dielectric in my very good E-dictionary that I am not sure they do exist in English actually.

[Vega]

By the way does anyone know where to find letters and mathematical operators and signs which I need for mathematical formulas?

Microsoft Office Word 2007.

Is there any software program in which I could create the operators by myself which I would like to use.

Yes. Here are some: Microsoft Student Graphing Calculator, MathLab, MathCAD.