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17_equations [2024-05-20 14:43] – nik17_equations [2024-08-12 11:04] (current) – nik
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 === Calculus === === Calculus ===
  
-$$\frac{\partial f}{\partial t} = \lim_{x\to\infty} =  \frac{f{(t+h)}- f{(t)}}{h}$$+$$\frac{\partial f}{\partial t} = \lim_{h\to\infty} =  \frac{f{(t+h)}- f{(t)}}{h}$$
  
  
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 === 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} 
-&\nabla\cdot\mathcal{E} = 0 +&\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}
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 ---- ----
-=== Schrodinger’s Equation ===+=== Schrödinger’s Equation === 
 + 
 +$$ih \frac{\delta}{\delta t}\Psi = H\Psi$$
  
  
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 === 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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