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17_equations [2024-05-05 11:08] nik17_equations [2024-08-12 11:04] (current) nik
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-==== Pythagorean Theorem ====+=== Pythagorean Theorem ===
  
 a2+b2=c2 a2+b2=c2
  
-==== Logarithms ====+---- 
 +=== Logarithms ===
  
 logxy=logx+logy logxy=logx+logy
  
-==== 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 ===
  
 Fgravity=Gm1m2r2 Fgravity=Gm1m2r2
  
-==== Complex Numbers ====+---- 
 +=== Complex Numbers ===
  
 i2=1 i2=1
  
-==== Euler’s Formula for Polyhedra ====+---- 
 +=== Euler’s Formula for Polyhedra ===
  
-==== Normal Distribution ====+$$V-E+F=2$$ 
 +---- 
 +=== Normal Distribution ===
  
-==== Wave Equation ====+$$\Phi(x)\frac{1}{\sqrt{2\pi\rho}} e^{\frac{(x-\mu)^2}{2\rho^2}}$$
  
-==== Fourier Transform ====+---- 
 +=== Wave Equation ===
  
-==== Navier-Stokes Equation ====+$$\frac{\partial^2 u}{\partial t^2} c^2 \frac{\partial^2 u}{\partial x^2}$$
  
-==== Maxwell’s Equations ====+---- 
 +=== Fourier Transform ===
  
-$$\begin{aligned}   +f(ω)=f(x)e2πixωdx 
-&\nabla\cdot\mathcal{E} = 0 + 
 +---- 
 +=== Navier-Stokes Equation === 
 + 
 +ρ(dvdt+vv)=p+T+f 
 + 
 +---- 
 +=== Maxwell’s Equations === 
 + 
 +$$\begin{aligned} 
 +&\nabla\cdot\mathcal{E} = 0
 &\nabla\cdot\mathcal{H} = 0 &\nabla\cdot\mathcal{H} = 0
 \end{aligned}$$ \end{aligned}$$
  
-$$\begin{aligned} +$$\begin{aligned}
 &\nabla\times\mathcal{E} = - \frac{1}{c}\frac{\partial\mathcal{H}}{\partial t} &\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} &\nabla\times\mathcal{H} = - \frac{1}{c}\frac{\partial\mathcal{E}}{\partial t}
 \end{aligned}$$ \end{aligned}$$
  
-==== Second Law of Thermodynamics ====+---- 
 +=== Second Law of Thermodynamics ===
  
 dS0 dS0
  
-==== Relativity ====+---- 
 +=== Relativity ===
  
 E=mc2 E=mc2
  
-==== Schrodinger’s Equation ====+---- 
 +=== Schrödinger’s Equation ===
  
 +ihδδtΨ=HΨ
  
-==== Information Theory ====+ 
 +---- 
 +=== Information Theory ===
  
 H=p(x)+logp(x) H=p(x)+logp(x)
  
-==== Chaos Theory ====+---- 
 +=== Chaos Theory ===
  
 xt+1=kxt(1xi) xt+1=kxt(1xi)
  
-==== Black-Scholes Equation ====+---- 
 +=== Black-Scholes Equation === 
 + 
 +$$\frac{1}{2}\sigma^2S^2 \frac{\delta^2 V}{\delta S^2} + rS \frac{\delta V}{\delta S} + \frac{\delta V}{\delta t} - rV 0$$
  
 +----
  
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  • Last modified: 2024-05-05 11:08
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