Expressing A Quantity In Polar Coordinates?

Homework Statement

Express the quantity ∂2/∂x2+∂2/∂y2 in polar coordinates.

x=ρcosφ
y=ρsinφ
ρ=sqrt(x2+y2)

The Attempt at a Solution

This is my first post, so I apologize for any weird looking equations, etc. I know that this is not a difficult problem, but I just cannot figure out exactly how to set it up. I don't know what function to differentiate for x and y... Any guidance would be appreciated. Thank you!

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jedishrfu
Mentor
Start by determining the first derivatives of x and y with respect to ##\rho## and ##\phi## and then repeat it for the second derivatives of x and y.

Also try learning latex when entering your symbols for consistency with other posts here at PF.

We quote our expressions with double # front and back: #.#.\rho.#.# (remove the dots to see the rho as a greek letter)

Here's the PF reference:

and here's a more extensive LaTex cheat sheet:

http://users.dickinson.edu/~richesod/latex/latexcheatsheet.pdf

Last edited:
SteamKing
Staff Emeritus
Homework Helper

Homework Statement

Express the quantity ∂2/∂x2+∂2/∂y2 in polar coordinates.

x=ρcosφ
y=ρsinφ
ρ=sqrt(x2+y2)

The Attempt at a Solution

This is my first post, so I apologize for any weird looking equations, etc. I know that this is not a difficult problem, but I just cannot figure out exactly how to set it up. I don't know what function to differentiate for x and y... Any guidance would be appreciated. Thank you!
2/∂x2+∂2/∂y2 is not a quantity.

It is the Laplacian expressed in cartesian coordinates. (otherwise known as the ∇2 operator)

http://hyperphysics.phy-astr.gsu.edu/hbase/lapl.html

jedishrfu