# Notation and Conventions¶

We choose the notation set forth in [WH88]. Their chapter has been the foundation of many research papers, is used by geophysicists world-wide, and it is clean and unambiguous.

## Vectors¶

• vectors and vectorial operators are bold:
• e.g., $$\mathbf{v}$$, $$\boldsymbol{\nabla\cdot}$$

• tensors are bold and underlined:
• e.g., $$\mathbf{\underline{v}}$$, $$\boldsymbol{\underline{\sigma}}$$

• time domain variable are lower case:
• e.g., $$\mathbf{e}$$, $$\mathbf{j}$$, $$\mathbf{h}$$, $$\mathbf{b}$$

• frequency domain variables are upper case:
• e.g., $$\mathbf{E}$$, $$\mathbf{J}$$, $$\mathbf{H}$$, $$\mathbf{B}$$

## Integrals¶

• Integrating a scalar function over a volume:
$\int_V f ~dv$
or over a closed volume:
$\oint_V f ~dv$
• Integrating a vector function over a surface:
$\int_S \mathbf{f} \cdot \mathbf{da} = \int_S \mathbf{f} \cdot \mathbf{\hat{n}} ~da$
or over a closed surface:
$\oint_S \mathbf{f} \cdot \mathbf{da} = \oint_S \mathbf{f} \cdot \mathbf{\hat{n}} ~da$
• Integrating a vector function over a curve:
$\int_C \mathbf{f} \cdot \mathbf{dl} = \int_C \mathbf{f} \cdot \mathbf{\hat{n}} ~dl$
or over a closed curve:
$\oint_C \mathbf{f} \cdot \mathbf{dl} = \oint_C \mathbf{f} \cdot \mathbf{\hat{n}} ~dl$

## Fourier Transform Convention¶

We also adopt their choice of sign in the Fourier Transform: $$e^{i\omega t}$$ time dependence.

(1)$F(\omega) = \int_{-\infty}^{\infty} f(t)e^{-i\omega t} dt$
(2)$f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\omega) e^{i\omega t} d\omega$