Laplacian in Slanted Coordinates

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SUMMARY

The discussion focuses on calculating the Laplacian operator ∇²F in a slanted coordinate system defined by u = y - x and v = y. The initial attempt at a solution incorrectly used derivatives with respect to r and s instead of the appropriate variables u and v. The correct formulation requires the application of the chain rule to transform the derivatives accordingly, ensuring that the Laplacian is expressed in terms of the new coordinates.

PREREQUISITES
  • Understanding of the Laplacian operator in multivariable calculus
  • Familiarity with coordinate transformations and the chain rule
  • Knowledge of partial derivatives and their applications
  • Basic concepts of vector calculus
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  • Study the derivation of the Laplacian in non-Cartesian coordinates
  • Learn about coordinate transformations in multivariable calculus
  • Explore the application of the chain rule in partial differentiation
  • Review examples of Laplacian calculations in different coordinate systems
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mathskier
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Whoops, I figured it out!
 
Last edited:
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mathskier said:

Homework Statement


Determine ∇2F in a coordinate system with u and v, where u=y-x and v=y.

Homework Equations


The Attempt at a Solution


I think that this is ∇2F= 2 (∂2F/∂r2 + ∂2F/(∂r ∂s))+∂2/∂s2. But I don't know how to check this... Is it correct?

Well, how did you get it? It can't be right, since the derivatives are with respect to r and s (whatever they are), not u and v.
 

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