(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I apologize in advance for my inability to present formal equations here. I'll do my best to be clear with the representation using simple text.

"Use the Jacobian Matrix to Prove Laplace's 2D Eq.: (partial^2 u)/(partial x^2) + (partial^2 u)/(partial y^2) = 0"

2. Relevant equations

Laplace Terms:

(partial u)/(partial x) = (partial v)/(partial y)

(partial u)/(partial y) = -(partial v)/(partial x)

3. The attempt at a solution

I attempted to place in the various Laplace Terms mentioned above into a 2x2 matrix, and find the determinant. However, this did not appear to work, as it resulted in:

det | (partial u)/(partial x), (partial u)/(partial y)|

| -(partial v)/(partial x), (partial v)/(partial y)|

= (partial^2 u)/(partial x^2) - (partial^2 u)/(partial y^2)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Using the Jacobian to Prove Laplace's 2D Eq.

**Physics Forums | Science Articles, Homework Help, Discussion**