Triple Integrals, cylindrical and spherical coord.

[TxAg]

i can get triple integrals to work when they are just in rectangular
coord. but i do not know how to make Mathcad rewrite the
integral for me in cylindrical coordinates. does anyone have a
program for this or the knowledge of the right commands?


TxAg

[TomGutman]

At the level that Mathcad works at integrals are not in any particular coordinate system -- rather they are in terms of particular variables. That these variables may represent coordinates in some coordinate system is something Mathcad neither knows nor cares about. It is up to you to set up the integral so that it represents what you want.

You can use the symbolic processor to rewrite a function expressed in one coordinate system to be expressed in a different coordinate system. Mathcad has some built in coordinate conversion functions (xyz2sph, sph2xyz, xyz2cyl, cyl2xyz), but the symbolic processor does not recognize them, so to use the symbolic processor you need to provide you own transformation functions. And when rewriting integrals, don't forget the Jacobian.

I have an old sheet doing line integrals in different coordinate systems at http://collab.mathsoft.com/read?45574,10e#45574 . This is not exactly what you are after, but it does show how to do coordinate transformations. This was done in MC11 (or possibly MC2001i -- it's quite old) and may or may not work in MC14.
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� � � � Tom Gutman

[TxAg]

so what your saying is mc will not transform the limits of
integration of a function from rectangular to cylindrical coord. or
what have you.

i havent checked out that sheet yet because my eyes are tired
from 4 hours of endg but ill check it in a bit an write back.

thank you for being so helpful i really do appreciate it

-Texas Aggie

[TomGutman]

>>so what your saying is mc will not transform the limits of integration of a function from rectangular to cylindrical coord. or what have you. <<

That is correct. Nor is this in general an easy problem. Indeed, it is often not even possible. Consider integrating over a spherical shell. Havine chosen a particular x and y, what are the limits for z? No simple limits. For most x and y values there are two distinct ranges of intersection. So the integral has to be split into at least two parts. But near the out edge there is a single interval. So the integral has to be set up differently for the different ranges of x and y.

That is why one learns about coordinate systems and how to set up integrals in different coordinates. Problems that are intractible in one coordinate system may become trivial in another. In spherical coordinates the integration over a spherical shell is nearly trivial.
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� � � � Tom Gutman