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圍棋口訣
========

一路易成眼
二路保眼活
三路駐守二
四路謀攻三
五路求外勢
六路怪棋翁
天元覓異數

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Density
=======

∫∫∫ d^3m = ∫∫∫ ρ_G dx dy dz

d^2(dm) = ρ_G dx dy dz ...(*)

∫∫∫ d^3q = ∫∫∫ ρ dx dy dz

d^2(dq) = ρ dx dy dz ...(**)

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Matrix and Derivative
=====================

du1 = ∂u1/∂x1 dx1 + ∂u1/∂x2 dx2 + ... + ∂u1/∂x_n dx_n ...(1)

du2 = ∂u2/∂x1 dx1 + ∂u2/∂x2 dx2 + ... + ∂u2/∂x_n dx_n ...(2)

...

du_m = ∂u_m/∂x1 dx1 + ∂u_m/∂x2 dx2 + ... + ∂u_m/∂x_n dx_n ...(m)

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Square Root of Energy
=====================

let
u = sqrt(E) ...(*)

du = ∂u/∂k dk ...(1), k = angular wavenumber

assume
u = A k + B + ε ...(2), where A, B are constants and ε ~= 0, over a small region.

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Energy and Frequency
====================

dE' = ∂E'/∂p' dp' ...(1)

assume
E' = A p' + B + ε ...(2), where A, B are constants and ε ~= 0, over a small region.

locally, when {
E' → E0' = constant

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Energy Wave Theory
==================

dv = ∂v/∂λ dλ ...(1)

assume
v = A λ + B + ε ...(2), where A, B are constants and ε ~= 0, over a small region.

locally, when {
v → v0 = constant

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Partial Derivative (1D)
=======================

let u = scalar
du = ∂u/∂x dx ...(1)

assume
u = A x + B + ε ...(2), where A, B are constants and ε ~= 0, over a small region.

locally, when {

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Velocity
========

let u = scalar
du = du
∂u/∂x dx = ∂u/∂t dt
∂/∂x(∂u/∂x dx) dx = ∂/∂t(∂u/∂t dt) dt
∂^2u/∂x^2 dx dx = ∂^2u/∂t^2 dt dt
∂^2u/∂x^2 dx^2 = ∂^2u/∂t^2 dt^2
...

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Phase Velocity
==============

有用的物理分析方法，是按已有（區域）的資訊，推測未知（區域）的效果。
所以，應該是 space invariant 及 time invariant 的。

let
u = u0 e^(i θ) ...(1)

assume locally

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五把尺
======

假設有五把尺。
尺一刻度用米。
尺二刻度用光秒。
尺三刻度用負光秒。
尺四刻度用虛光秒。
尺五刻度用負虛光秒。