Mac Dude

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These are questions asked by Mac Dude

I have an expression like this:

Since it is linear I want Maple to rewrite it into this:

(with the benefit that Maple then can solve it at least up to a point). i have tried to conceive a rule to do that but got stuck relatively quickly. Does anybody have a way to do this (in some genrality)?

Thanks,

Mac Dude.

 

Here is a problem I have with the Nabla operator:

I am working on a demonstration involving Maxwell's equations:

restart:with(Physics[Vectors]);
Setup(mathematicalnotation = true);
# Maxwell's eqn
M4 := `&x`(Nabla, B1_(x, y, z, t)) = mu*epsilon*(diff(E1_(x, y, z, t), t));

eval(subs(B1_(x,y,z,t)=Bxx(x,y,z,t)*_i+Bzz(x,y,z,t)*_k,M4)); # transverse magnetic field, no longitudinal (j) component

# Ok, this one is as expected.

eval(subs(B1_(x,y,z,t)=Bxx(x,y,z,t)*_i+Bzz(x,y,z,t)*_k,M4)) assuming real;

# Hmm... why is this zero?

eval assuming real seems to make them all zero. In this little example, Bxx and Bzz are just arbitrary functions and therefore the result cannot be zero in general. The bother here is that I later use a parametrization of the field (the Bxx and Bzz) which in fact does make curl(B) = 0. I wanted Maple to demonstrate that the parametrization does that, but it appears i can make the result zero for any B-field, which sort-of defeats the purpose. If I don't assume real, with the other parametrization Maple isn't getting anywhere...

So, how can I get correct results while declaring variables to be real when they are... ?

Thanks,

M.D.

Maxwell_test.mw

In Physics[Vectors] the operation ChangeBasis exists to change between different coordinate systems (Carthesian, cylindrical and spherical). The cylindrical system uses the third coordinate (_k) as its axis.

As it happens, in my work the axis of the cylindrial system should be the 2nd one (_j). I do not want to reformulate everything as this would become non-standard and confusing. I am wondering whether it is conceivable to "retrofit" the Physics package to allow for that. At issue are not so much the formulae; I can do the transformation "by hand", but that is a bit clumsy and I am looking for a way to have this integrated better in the Physics package so that all other operations (e.g. Nabla) do the expected.

I have looked for and not found something like an "addBasis" command. Am I missing something obvious here? I should add that some of my work happens on Maple 15 (Mac OS X PPC so no upgrade possible); if something like this was added recently I may have missed it, although I do have access to Maple 17 as well so I could use that version for this particular problem. Is the source of Physics actually open?

TIA,

Mac Dude

I am trying to get a Fourier transform of a Gaussian:

so I say

and get

The Fouriertransform of a Gaussian is well known and the result I expect is something like

exp(1/2*sigma^2*omega^2)

ignoring normalizations & other factors. I know that I can add functions to inttrans, but I kind-of expected inttrans[fourier] to know how to transform a Gaussian, it is a commonly used transformation. Even if I set phi0 to 0 it does not produce anything useful.

???

Mac Dude

I have the following d.e.:

I need to change the s variable into a different one, where the new variable is defined by

(the old s shows up in the limit of the integral)

I tried dchange, but it chokes on this as I don't have an explicit representation of s in terms of Theta.

(I know the overall solution as other people smarter than me have solved this a long time ago, but I 'd like to have the derivation to understand it).

Mac Dude

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