1. Limited time only! Sign up for a free 30min personal 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!

Laplace inverse of a particular function - trouble following text (Carslaw & Jaeger)

  1. Feb 27, 2009 #1
    Hello all,

    I've been following along in Carslaw & Jaeger's book on heat conduction. Section 14.7 p. 366 we're presented with the function:

    \overline{v} = \frac{sinh(qr)sinhq(a-r')}{4\pi r\cdot r' \cdot k \cdot q sinh(qa)}

    It's simply stated that the "Inversion Theorem" is used to do the inverse laplace transform to obtain v as:

    v = \frac{1}{2\pi\cdot a \cdot r \cdot r'} \Sigma_{n = 1}^{\infty} e^{-k\cdot n^2 \cdot \pi^2 \cdot t / a^2}\cdot sin(\frac{n\cdot\pi\cdot r}{a})\cdot sin(\frac{n\cdot\pi\cdot r'}{a})

    I'm having trouble seeing how this works out. The reason why I ask is because I'm trying to solve a related problem that is of significant importance to me for my own research.

    Any help is very greatly appreciated.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted