# 伟大的公式

## 2012-07-22 12:49:52

• No.10 圆周长公式（The Length of the Circumference of a Circle） $c=2 \pi r$

• No.9 傅立叶变换（The Fourier Transform） $\hat {F} (\xi)=\int_{-\infty}^{+\infty} f(x) e^{-2 \pi i \xi x} dx$

• No.8 德布罗意关系式（The de Broglie Relations） $\boldsymbol{p} = \hbar \boldsymbol{k} \;\;\;\; E=\hbar \omega$

• No.7 1+1=2 $1+1=2$

• No.6 薛定谔方程（The Schrödinger’s Equation） $\hat{H}\Psi = i\hbar {\partial{ \Psi} \over \partial t }$

• No.5 质能方程（Mass-energy Equivalence） $E=mc^2$

• No.4 勾股定理/毕达哥拉斯定理（Pythagorean Theorem） $a^2+b^2=c^2$

• No.3 牛顿第二定律（Newton’s Second Law of Motion） $\mathbf{F} = m \mathbf{a}$

• No.2 欧拉公式（Euler’s Identity） $e^{i\pi}+1=0$

• No.1 麦克斯韦方程组（The Maxwell’s Equations）

微分形式： $\nabla \cdot \mathbf{E} = {\rho \over \varepsilon} \\ \nabla \cdot \mathbf{B} = 0 \\ \nabla \times \mathbf{E} = -{ \partial \mathbf{B} \over \partial t} \\ \nabla \times \mathbf{B} = \mu \mathbf{J} + \mu \varepsilon {\partial \mathbf{E} \over \partial t }$

积分形式： $\oint_{\partial \Omega} \mathbf{E} \cdot d\mathbf{S} = {Q \over \varepsilon} \\ \oint_{\partial \Omega} \mathbf{B} \cdot d\mathbf{S} = 0 \\ \oint_{\partial \Sigma} \mathbf{E} \cdot d\mathbf{l} = - \iint_\Sigma {\partial \mathbf{B} \over \partial t} \cdot d\mathbf{S} \\ \oint_{\partial \Sigma} \mathbf{B} \cdot d\mathbf{l} = \mu I + \mu\varepsilon \iint_\Sigma {\partial \mathbf{E} \over \partial t} \cdot d\mathbf{S}$

1. Maxwell’s four equations describing how an electromagnetic field varies in space and time.

2. Euler’s equation of momentum-flow and force-density in fluid dynamics. ${\partial \boldsymbol{v} \over \partial t } + (\boldsymbol{v} \cdot \nabla) \boldsymbol{v} = -{\nabla P \over \rho} + \boldsymbol{f}$

3. Newton’s Second Law (F=ma) - ‘The rate of change of momentum of a body is equal to the resultant force acting on the body and is in the same direction’.

4. Pythagoras’s Theorum (a^2+b^2=c^2;) - In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

5. Schrödinger’s equation describing the time-dependence of quantum mechanical systems.

6. Boltzmann equation describing the statistical distribution of particles in a fluid. ${\partial f \over \partial t} +\boldsymbol{v} \cdot \nabla f + {\boldsymbol{p} \over m} \cdot \nabla f = ({\partial f \over \partial t})_{coll}$

7. Principle of Least Action (or Principle of stationary action) $\delta \int_{t_1}^{t_2} L(q,\dot{q},t) dt=0$

8. De Broglie’s equation - showing that the wavelength is inversely proportional to the momentum of a particle and that the frequency is directly proportional to the particle’s kinetic energy.

9. Fourier Transformation - an integral transform that re-expresses a function in terms of sinusoidal basis functions.

10. Einstein’s field equations for General Relativity. $R_{\mu\nu}-{1 \over 2}g_{\mu\nu}R+g_{\mu\nu}\Lambda={8\pi G \over c^4} T_{\mu\nu}$

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