MHB Understanding the Harmonic Function Problem

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The discussion centers on the Harmonic Function Problem, specifically the mathematical definition of a harmonic function, which requires that the sum of the second partial derivatives with respect to x and y equals zero. Participants emphasize understanding this condition to solve related problems effectively. Clarification is sought on the concept of harmonic functions, indicating a struggle with the underlying principles. The conversation highlights the importance of grasping the mathematical formulation to progress in solving harmonic function questions. Overall, a clear understanding of the harmonic condition is essential for tackling these types of mathematical problems.
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Please help me I am struggle with this question
Thank you in advance
 
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Well, do you know what a Harmonic Function is?

In this case, to be Harmonic, you would need $\displaystyle \begin{align*} \frac{\partial ^2 u}{\partial x^2} + \frac{\partial ^2 u}{\partial y^2} = 0 \end{align*}$...
 
Prove It said:
Well, do you know what a Harmonic Function is?

In this case, to be Harmonic, you would need $\displaystyle \begin{align*} \frac{\partial ^2 u}{\partial x^2} + \frac{\partial ^2 u}{\partial y^2} = 0 \end{align*}$...
Thank you for helping me
 

Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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