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--- 17_equations [2024-05-05 10:45] – [Calculus] nik
+++ 17_equations [2024-05-20 14:39] – nik
@@ Line 4: / Line 4: @@
-==== 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 ====
 $$\frac{\partial f}{\partial t} = \lim_{x\to\infty} =  \frac{f{(t+h)}- f{(t)}}{h}$$
-==== Newton’s Law of Gravity ====
+=== Newton’s Law of Gravity ===
-${F}_\text{gravity}=G\frac{m_{1}m_{2}}{r^{2}}$
-==== 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 Equation ===
-==== Fourier Transform ====
+=== Maxwell’s Equations ===
-==== Navier-Stokes Equation ====
+$$\begin{aligned}
+&\nabla\cdot\mathcal{E} = 0
+&\nabla\cdot\mathcal{H} = 0
+\end{aligned}$$
-==== Maxwell’s Equations ====
+$$\begin{aligned}
+&\nabla\times\mathcal{E} = - \frac{1}{c}\frac{\partial\mathcal{H}}{\partial t}
+&\nabla\times\mathcal{H} = - \frac{1}{c}\frac{\partial\mathcal{E}}{\partial t}
+\end{aligned}$$
-==== 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 ===