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start of docs for e-formulation

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Lindsey Heagy
2014-04-05 13:19:21 -07:00
parent e26aa607a3
commit beb2fa1a58
2 changed files with 22 additions and 11 deletions
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docs/api_FDEM.rst
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@@ -19,7 +19,7 @@ Electromagnetic phenomena are governed by Maxwell's equations. They describe the
Fourier Transform Convention
----------------------------
In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the \\(e^{i \\omega t} \\)\\ convention, so we define our Fourier Transform pair as
In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the \\(e^{i \\omega t} \\) convention, so we define our Fourier Transform pair as
.. math ::
F(\omega) = \int_{-\infty}^{\infty} f(t) e^{- i \omega t} dt \\
@@ -76,7 +76,7 @@ For a more complete discussion of physical properties see `GPG <http://www.eos.u
Quasi-static Approximation
--------------------------
For the frequency range typical of most geophysical surveys, the contribution of the electric displacement is negligible compared to the electric current density. In this case, we use the \\(\\emph{Quasi-static approximation}\\) and assume that this term can be neglected, giving
For the frequency range typical of most geophysical surveys, the contribution of the electric displacement is negligible compared to the electric current density. In this case, we use the Quasi-static approximation and assume that this term can be neglected, giving
.. math ::
\nabla \times \vec{E} = -i \omega \vec{B} \\