Laplace and Poisson Equation in oblate and prolate spheroids

kingdavid
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Hi everyone,
I have been trying to solve both laplace and poisson equation using method of separation of variable but is giving me a hard time.
Pls can anyone refer me to any textbook that solve this problem in great detail?

Thanks
 
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Morse and Feshbach solve these problems in all separable coordinate systems in their books Methods of Theoretical Physics.
 
Hi Marcus,
Thank you for your response to my request.
I will go and find the book.
I quite appreciate it.

Kingdavid
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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