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17_equations [2024-05-05 10:45] – [Calculus] nik | 17_equations [2024-08-12 11:04] (current) – nik | ||
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- | ==== Pythagorean Theorem | + | === Pythagorean Theorem === |
- | a2+b2=c2 | + | $$a^2 + b^2 = c^2$$ |
- | ==== Logarithms | + | ---- |
+ | === Logarithms === | ||
- | logxy=logx+logy | + | $$log{xy} = log{x} + log{y}$$ |
- | ==== Calculus ==== | + | ---- |
- | ∂f∂t=limx→∞=f(t+h)−f(t)h | + | === Calculus === |
+ | ∂f∂t=limh→∞=f(t+h)−f(t)h | ||
- | ==== Newton’s Law of Gravity ==== | ||
- | Fgravity=Gm1m2r2 | ||
- | ==== Complex Numbers ==== | ||
- | $i^2=-1$ | + | ---- |
+ | === Newton’s Law of Gravity === | ||
- | ==== Euler’s Formula for Polyhedra ==== | + | $${F}_\text{gravity}=G\frac{m_{1}m_{2}}{r^{2}}$$ |
- | ==== Normal Distribution ==== | + | ---- |
+ | === Complex Numbers | ||
- | ==== Wave Equation ==== | + | $$i^2=-1$$ |
- | ==== Fourier Transform ==== | + | ---- |
+ | === Euler’s Formula for Polyhedra | ||
- | ==== Navier-Stokes Equation ==== | + | $$V-E+F=2$$ |
+ | ---- | ||
+ | === Normal Distribution | ||
- | ==== Maxwell’s Equations ==== | + | $$\Phi(x)= \frac{1}{\sqrt{2\pi\rho}} e^{\frac{(x-\mu)^2}{2\rho^2}}$$ |
- | ==== Second Law of Thermodynamics ==== | + | ---- |
+ | === Wave Equation | ||
- | $dS\geq0$ | + | $$\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}$$ |
- | ==== Relativity ==== | + | ---- |
+ | === Fourier Transform | ||
- | $E=mc^2$ | + | $$f(\omega) |
- | ==== Schrodinger’s | + | ---- |
+ | === Navier-Stokes | ||
+ | ρ(dvdt+v⋅v∇)=−∇p+∇⋅T+f | ||
- | ==== Information Theory ==== | + | ---- |
+ | === Maxwell’s Equations | ||
- | $H=-\sum p(x) + log{p(x)}$ | + | $$\begin{aligned} |
+ | & | ||
+ | & | ||
+ | \end{aligned}$$ | ||
- | ==== Chaos Theory ==== | + | $$\begin{aligned} |
+ | & | ||
+ | & | ||
+ | \end{aligned}$$ | ||
- | $x_{t+1} = kx_t(1-x_i)$ | + | ---- |
+ | === Second Law of Thermodynamics === | ||
- | ==== Black-Scholes Equation ==== | + | dS≥0 |
+ | ---- | ||
+ | === Relativity === | ||
+ | |||
+ | E=mc2 | ||
+ | |||
+ | ---- | ||
+ | === Schrödinger’s Equation === | ||
+ | |||
+ | ihδδtΨ=HΨ | ||
+ | |||
+ | |||
+ | ---- | ||
+ | === Information Theory === | ||
+ | |||
+ | H=−∑p(x)+logp(x) | ||
+ | |||
+ | ---- | ||
+ | === Chaos Theory === | ||
+ | |||
+ | xt+1=kxt(1−xi) | ||
+ | |||
+ | ---- | ||
+ | === Black-Scholes Equation === | ||
+ | |||
+ | 12σ2S2δ2VδS2+rSδVδS+δVδt−rV=0 | ||
+ | |||
+ | ---- | ||