1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Complex Analysis Harmonic functions

  1. Nov 7, 2016 #1
    Suppose u(x,y) and v(x,y) are harmonic on G and c is an element of R. Prove u(x,y) + cv(x,y) is also harmonic.

    I tried using the Laplace Equation of Uxx+Uyy=0

    I have:
    du/dx=Ux
    d^2u/dx^2=Uxx

    du/dy=Uy
    d^2u/dy^2=Uyy

    dv/dx=cVx
    d^2v/dx^2=cVxx

    dv/dy=cVy
    d^2v/dy^2=cVyy
    I'm not really sure how to prove these are harmonic...am I missing a relationship?
     
  2. jcsd
  3. Nov 7, 2016 #2

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    Define w(x,y) = u(x,y) + cv(x,y) and calculate wxx + wyy. Basic properties of the partial derivative should give you the answer.
     
  4. Nov 8, 2016 #3
    Wow, that's a really good idea. I was trying to do the harmonic conjugate but was getting nowhere. Thank you!
     
  5. Nov 10, 2016 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    do you understand what it means to say that differentiation is a linear operator?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted