Thank you for your knowledge of maths and science, and for the good cooperation.(adsbygoogle = window.adsbygoogle || []).push({});

First of all, may I asked a question on solving partial differential equations using hyper complex variables?

Please can you briefly explain why the constants of integration in solving partial differential equations (x,t) within the 4D hyper-complex domain are not arbitrary functions of x,t, but are actual constants which should not be differentiated when finding derivatives.

If we have three constants for 1 initial + 2 boundary conditions, and we want to set t=0, then we must leave x as it is. Therefore the arbitrary constants are instead arbitrary functions which depend on either x or t. Therefore, I do not understand why they are not differentiated in hypercomplex variables. Or is it appropriate to take any x?

May I pop in another minor question? In Z=1x+iy+ jz+kct, I know c is the characteristic speed of the medium, what if we were dealing with water, or peroleum? Does this mean that that number was in mind when deriving this transformation? I am solving the Burgers equation, which does not require scaling the time, so why should I scale it here?

Thanks a million

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# Partial differntials with hypercomplex numbers

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