I am studying online course notes from University of Waterloo on 'Analytical mathematics in geology' in which the author describes a 'modified fourier transform' which can be used to incorporate 3rd kind of boundary conditions. The formula is(adsbygoogle = window.adsbygoogle || []).push({});

## \Gamma \small[ f(x) \small] = \bar{f}(a) = \int_{0}^{\infty } f(x) [a \cos(ax) + h\sin(ax)] dx ##

where $$ \Gamma $$ be the fourier operator.

with operational property

##\Gamma [\frac{d^2f}{dx^2}] = -a^2 \bar{f}(a) - a [ \frac{df}{dx}|_{x=0} - hf|_{x=0} ]##

I am trying to look for the detailed derivation of this equation in literature but have not found so far! Can anybody tell me in which book I can find detailed derivation of this formula and possibly with application?

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

Dismiss Notice

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!

# A Fourier Transform for 3rd kind of boundary conditions?

Tags:

Have something to add?

Draft saved
Draft deleted

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