- #1
jaychay
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Understanding the Harmonic Function Problem
In summary, a harmonic function is a smooth and continuous mathematical function that satisfies the Laplace equation. It has various applications in science, particularly in physics and engineering, and is used to describe the behavior of electric and magnetic fields, fluid flow, and heat conduction. The harmonic function problem refers to the task of finding a harmonic function that satisfies certain boundary conditions, and there are various techniques, such as separation of variables and the method of conformal mapping, used to solve it. However, the problem can only be solved for specific, well-defined boundary conditions that satisfy certain criteria. In some cases, additional constraints or assumptions may be needed to find a unique solution.
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- #2
Prove It
Gold Member
MHB
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Well, do you know what a Harmonic Function is?
In this case, to be Harmonic, you would need $\displaystyle \begin{align*} \frac{\partial ^2 u}{\partial x^2} + \frac{\partial ^2 u}{\partial y^2} = 0 \end{align*}$...
In this case, to be Harmonic, you would need $\displaystyle \begin{align*} \frac{\partial ^2 u}{\partial x^2} + \frac{\partial ^2 u}{\partial y^2} = 0 \end{align*}$...
- #3
jaychay
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Thank you for helping meProve It said: