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# Curl function - help!

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1. I'm trying to find a function that fits the following conditions:

And if :

(i.e. A(r) has to be zero at r = 0 and r = 1, and B(r) has to have a maximum at r = 0 and has to be 0 at r = 1, and both functions must be greater than or equal to zero for r between 0 and 1).

Is this possible? So far I've been using a function based on as which satisfies all of the above apart from but I really need to find something that fulfils this condition too.
2. (Original post by Plagioclase)
I'm trying to find a function that fits the following conditions:

And if :

(i.e. A(r) has to be zero at r = 0 and r = 1, and B(r) has to have a maximum at r = 0 and has to be 0 at r = 1, and both functions must be greater than or equal to zero for r between 0 and 1).

Is this possible? So far I've been using a function based on as which satisfies all of the above apart from but I really need to find something that fulfils this condition too.
Here's a hint: take your differential expression for B in terms of A and invert it by integration to get A in terms of B. Then note that A(1) is an integral of stuff that is strictly poisitive and therefore cannot be zero.
3. (Original post by Gregorius)
Here's a hint: take your differential expression for B in terms of A and invert it by integration to get A in terms of B. Then note that A(1) is an integral of stuff that is strictly poisitive and therefore cannot be zero.
Ugh silly me, thanks for that!

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