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17_equations [2024-05-05 10:45] – [Calculus] nik | 17_equations [2024-05-05 11:08] (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 ==== | ==== 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 ==== | ||
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==== Maxwell’s Equations ==== | ==== Maxwell’s Equations ==== | ||
+ | |||
+ | $$\begin{aligned} | ||
+ | & | ||
+ | & | ||
+ | \end{aligned}$$ | ||
+ | |||
+ | $$\begin{aligned} | ||
+ | & | ||
+ | & | ||
+ | \end{aligned}$$ | ||
==== 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 ==== | ||
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==== 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 ==== | ||