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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| 17_equations [2024-05-20 14:39] – nik | 17_equations [2024-08-12 11:04] (current) – nik | ||
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| $$a^2 + b^2 = c^2$$ | $$a^2 + b^2 = c^2$$ | ||
| + | ---- | ||
| === Logarithms === | === Logarithms === | ||
| $$log{xy} = log{x} + log{y}$$ | $$log{xy} = log{x} + log{y}$$ | ||
| + | ---- | ||
| === Calculus === | === Calculus === | ||
| - | $$\frac{\partial f}{\partial t} = \lim_{x\to\infty} = \frac{f{(t+h)}- f{(t)}}{h}$$ | + | $$\frac{\partial f}{\partial t} = \lim_{h\to\infty} = \frac{f{(t+h)}- f{(t)}}{h}$$ |
| + | ---- | ||
| === Newton’s Law of Gravity === | === Newton’s Law of Gravity === | ||
| $${F}_\text{gravity}=G\frac{m_{1}m_{2}}{r^{2}}$$ | $${F}_\text{gravity}=G\frac{m_{1}m_{2}}{r^{2}}$$ | ||
| + | ---- | ||
| === Complex Numbers === | === Complex Numbers === | ||
| $$i^2=-1$$ | $$i^2=-1$$ | ||
| + | ---- | ||
| === Euler’s Formula for Polyhedra === | === Euler’s Formula for Polyhedra === | ||
| + | $$V-E+F=2$$ | ||
| + | ---- | ||
| === Normal Distribution === | === Normal Distribution === | ||
| + | $$\Phi(x)= \frac{1}{\sqrt{2\pi\rho}} e^{\frac{(x-\mu)^2}{2\rho^2}}$$ | ||
| + | |||
| + | ---- | ||
| === Wave Equation === | === Wave Equation === | ||
| + | $$\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}$$ | ||
| + | |||
| + | ---- | ||
| === Fourier Transform === | === Fourier Transform === | ||
| + | $$f(\omega) = \int_{\infty}^{\infty}f(x)e^{-2\pi i x \omega} \text{d}x$$ | ||
| + | |||
| + | ---- | ||
| === Navier-Stokes Equation === | === Navier-Stokes Equation === | ||
| + | $$\rho\left(\frac{d\text{v}}{dt} + \text{v} \cdot \text{v}\nabla \right) = -\nabla p + \nabla \cdot \text{T} + \text{f}$$ | ||
| + | |||
| + | ---- | ||
| === Maxwell’s Equations === | === Maxwell’s Equations === | ||
| - | $$\begin{aligned} | + | $$\begin{aligned} |
| - | & | + | & |
| & | & | ||
| \end{aligned}$$ | \end{aligned}$$ | ||
| - | $$\begin{aligned} | + | $$\begin{aligned} |
| & | & | ||
| & | & | ||
| \end{aligned}$$ | \end{aligned}$$ | ||
| + | ---- | ||
| === Second Law of Thermodynamics === | === Second Law of Thermodynamics === | ||
| $$dS\geq0$$ | $$dS\geq0$$ | ||
| + | ---- | ||
| === Relativity === | === Relativity === | ||
| $$E=mc^2$$ | $$E=mc^2$$ | ||
| - | === Schrodinger’s Equation === | + | ---- |
| + | === Schrödinger’s Equation === | ||
| + | $$ih \frac{\delta}{\delta t}\Psi = H\Psi$$ | ||
| + | |||
| + | ---- | ||
| === Information Theory === | === Information Theory === | ||
| $$H=-\sum p(x) + log{p(x)}$$ | $$H=-\sum p(x) + log{p(x)}$$ | ||
| + | ---- | ||
| === Chaos Theory === | === Chaos Theory === | ||
| $$x_{t+1} = kx_t(1-x_i)$$ | $$x_{t+1} = kx_t(1-x_i)$$ | ||
| + | ---- | ||
| === Black-Scholes Equation === | === Black-Scholes Equation === | ||
| + | $$\frac{1}{2}\sigma^2S^2 \frac{\delta^2 V}{\delta S^2} + rS \frac{\delta V}{\delta S} + \frac{\delta V}{\delta t} - rV = 0$$ | ||
| + | |||
| + | ---- | ||