==== 17 Equations ====

In his book, In Pursuit of the Unknown: 17 Equations That Changed the World, Ian Stewart discusses each equation engagingly and practically...


=== Pythagorean Theorem ===

$$a^2 + b^2 = c^2$$

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=== Logarithms ===

$$log{xy} = log{x} + log{y}$$

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=== Calculus ===

$$\frac{\partial f}{\partial t} = \lim_{h\to\infty} =  \frac{f{(t+h)}- f{(t)}}{h}$$


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=== Newton’s Law of Gravity ===

$${F}_\text{gravity}=G\frac{m_{1}m_{2}}{r^{2}}$$

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=== Complex Numbers ===

$$i^2=-1$$

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=== Euler’s Formula for Polyhedra ===

$$V-E+F=2$$
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=== Normal Distribution ===

$$\Phi(x)= \frac{1}{\sqrt{2\pi\rho}} e^{\frac{(x-\mu)^2}{2\rho^2}}$$

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=== Wave Equation ===

$$\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}$$

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=== Fourier Transform ===

$$f(\omega) = \int_{\infty}^{\infty}f(x)e^{-2\pi i x \omega} \text{d}x$$

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=== Navier-Stokes Equation ===

$$\rho\left(\frac{d\text{v}}{dt} + \text{v} \cdot \text{v}\nabla \right) = -\nabla p + \nabla \cdot \text{T} + \text{f}$$

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=== Maxwell’s Equations ===

$$\begin{aligned}
&\nabla\cdot\mathcal{E} = 0
&\nabla\cdot\mathcal{H} = 0
\end{aligned}$$

$$\begin{aligned}
&\nabla\times\mathcal{E} = - \frac{1}{c}\frac{\partial\mathcal{H}}{\partial t}
&\nabla\times\mathcal{H} = - \frac{1}{c}\frac{\partial\mathcal{E}}{\partial t}
\end{aligned}$$

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=== Second Law of Thermodynamics ===

$$dS\geq0$$

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=== Relativity ===

$$E=mc^2$$

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=== Schrödinger’s Equation ===

$$ih \frac{\delta}{\delta t}\Psi = H\Psi$$


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=== Information Theory ===

$$H=-\sum p(x) + log{p(x)}$$

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=== Chaos Theory ===

$$x_{t+1} = kx_t(1-x_i)$$

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=== Black-Scholes Equation ===

$$\frac{1}{2}\sigma^2S^2 \frac{\delta^2 V}{\delta S^2} + rS \frac{\delta V}{\delta S} + \frac{\delta V}{\delta t} - rV = 0$$

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