From beb2fa1a58f05f4f266acf0b1af213fe8156e9a6 Mon Sep 17 00:00:00 2001
From: Lindsey Heagy <lindseyheagy@gmail.com>
Date: Sat, 5 Apr 2014 13:19:21 -0700
Subject: [PATCH] start of docs for e-formulation

---
 docs/api_FDEM.rst     |  4 ++--
 simpegEM/FDEM/FDEM.py | 29 ++++++++++++++++++++---------
 2 files changed, 22 insertions(+), 11 deletions(-)

diff --git a/docs/api_FDEM.rst b/docs/api_FDEM.rst
index ab6dc611..faa93cd0 100644
--- a/docs/api_FDEM.rst
+++ b/docs/api_FDEM.rst
@@ -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} \\
diff --git a/simpegEM/FDEM/FDEM.py b/simpegEM/FDEM/FDEM.py
index 8074fdba..521e74c0 100644
--- a/simpegEM/FDEM/FDEM.py
+++ b/simpegEM/FDEM/FDEM.py
@@ -9,16 +9,13 @@ def omega(freq):
 
 class BaseProblemFDEM(Problem.BaseProblem):
     """
-        We start with the E-formulation Maxwell's equations in the frequency domain:
-        .. math ::
+        We start by looking at Maxwell's equations in the electric field \\(\\vec{E}\\) and the magnetic flux density \\(\\vec{B}\\):
+
+        .. math::
+
             \\nabla \\times \\vec{E} + i \\omega \\vec{B} = 0 \\\\
             \\nabla \\times \\mu^{-1} \\vec{B} - \\sigma \\vec{E} = \\vec{J_s}
-        By eliminating the magnetic flux density using
-        .. math ::
-            \\vec{B} = \\frac{-1}{i\\omega}\\nabla\\times\\vec{E},
-        we can write Maxwell's equations as a second order system in \\ \\vec{E} \\ only:
-        .. math ::
-            \\nabla \\times \\mu^{-1} \\nabla \\times \\vec{E} + i \\omega \\sigma \\vec{E} = \\vec{J_s}
+
     """
     def __init__(self, model, **kwargs):
         Problem.BaseProblem.__init__(self, model, **kwargs)
@@ -169,7 +166,21 @@ class BaseProblemFDEM(Problem.BaseProblem):
 
 class ProblemFDEM_e(BaseProblemFDEM):
     """
-        Solving for e!
+        By eliminating the magnetic flux density using
+
+        .. math::
+
+            \\vec{B} = \\frac{-1}{i\\omega}\\nabla\\times\\vec{E},
+
+        we can write Maxwell's equations as a second order system in \\ \\vec{E} \\ only:
+
+        .. math::
+
+            \\nabla \\times \\mu^{-1} \\nabla \\times \\vec{E} + i \\omega \\sigma \\vec{E} = \\vec{J_s}
+
+        This is the definition of the Forward Problem using the E-formulation of Maxwell's equations.
+
+
     """
     solType = 'e'