Math contents sample

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This is a sample file to create math contents.

1.1. Mathematical Discription.

For example, this is a representation of Maxwell's equations.

\begin{aligned} \nabla \circ E & = \frac{ρ}{ε_{0}}, \\ \nabla \circ B & = 0, \\ \nabla \times E & = - \frac{\partial B}{\partial t}, \\ \nabla \times B & = μ_{0} J + μ_{0} ε_{0} \frac{\partial E}{\partial t} . \end{aligned}

(1.1)

It is able to derive these relations for

z := x + i y

and

Y := - sgn (y)

f (z) := \frac{n!}{2 π} (i z)^{- n - 1} e^{2 i δ} \Rightarrow {\begin{array}{rcl} Re f (z) & = & \frac{(Y ʹ)^{n + 1}}{4 π} \int ∣ ξ ∣^{n} e^{ξ Y + Y ʹ i sgn (ξ) 2 δ - i ξ x} d ξ, \\ Im f (z) & = & - \frac{(Y ʹ)^{n}}{4 π} \int ∣ ξ ∣^{n} i sgn (ξ) e^{ξ Y + Y ʹ i sgn (ξ) 2 δ - i ξ x} d ξ . \end{array}

(1.2)