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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums - The Fusion of Science and Community**

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!

# I Complex Analysis Harmonic functions

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Complex Analysis Harmonic | Date |
---|---|

I Map from space spanned by 2 complex conjugate vars to R^2 | Nov 23, 2017 |

I Help with expression ##F(it)-F(-it)## in the Abel-Plana form | Aug 7, 2017 |

I Difference between complex and real analysis | May 26, 2017 |

I Complex analysis proof | May 26, 2017 |

Calculating Harmonic Sums using Residues | Dec 30, 2014 |

**Physics Forums - The Fusion of Science and Community**