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17_equations [2024-05-05 10:45] – [Calculus] nik | 17_equations [2024-05-20 14:43] (current) – nik | ||
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- | ==== Pythagorean Theorem | + | === Pythagorean Theorem === |
- | $a^2 + b^2 = c^2$ | + | $$a^2 + b^2 = c^2$$ |
- | ==== Logarithms | + | ---- |
+ | === Logarithms === | ||
- | $log{xy} = log{x} + log{y}$ | + | $$log{xy} = log{x} + log{y}$$ |
+ | |||
+ | ---- | ||
+ | === Calculus === | ||
- | ==== Calculus ==== | ||
$$\frac{\partial f}{\partial t} = \lim_{x\to\infty} = \frac{f{(t+h)}- f{(t)}}{h}$$ | $$\frac{\partial f}{\partial t} = \lim_{x\to\infty} = \frac{f{(t+h)}- f{(t)}}{h}$$ | ||
- | ==== Newton’s Law of Gravity | + | ---- |
- | ${F}_\text{gravity}=G\frac{m_{1}m_{2}}{r^{2}}$ | + | === Newton’s Law of Gravity === |
- | ==== Complex Numbers ==== | + | |
+ | $${F}_\text{gravity}=G\frac{m_{1}m_{2}}{r^{2}}$$ | ||
+ | |||
+ | ---- | ||
+ | === Complex Numbers === | ||
+ | |||
+ | $$i^2=-1$$ | ||
+ | |||
+ | ---- | ||
+ | === Euler’s Formula for Polyhedra | ||
- | $i^2=-1$ | + | ---- |
+ | === Normal Distribution === | ||
- | ==== Euler’s Formula for Polyhedra ==== | + | ---- |
+ | === Wave Equation | ||
- | ==== Normal Distribution ==== | + | ---- |
+ | === Fourier Transform | ||
- | ==== Wave Equation | + | ---- |
+ | === Navier-Stokes | ||
- | ==== Fourier Transform ==== | + | ---- |
+ | === Maxwell’s Equations | ||
- | ==== Navier-Stokes Equation ==== | + | $$\begin{aligned} |
+ | & | ||
+ | & | ||
+ | \end{aligned}$$ | ||
- | ==== Maxwell’s Equations ==== | + | $$\begin{aligned} |
+ | & | ||
+ | & | ||
+ | \end{aligned}$$ | ||
- | ==== Second Law of Thermodynamics | + | ---- |
+ | === Second Law of Thermodynamics === | ||
- | $dS\geq0$ | + | $$dS\geq0$$ |
- | ==== Relativity | + | ---- |
+ | === Relativity === | ||
- | $E=mc^2$ | + | $$E=mc^2$$ |
- | ==== Schrodinger’s Equation | + | ---- |
+ | === Schrodinger’s Equation === | ||
- | ==== 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 === | ||