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Curl of a Vector Field

$∇→×F→=(∂Fz∂y−∂Fy∂z)i+(∂Fx∂z−∂Fz∂x)j+(∂Fy∂x−∂Fx∂y)k$

Definition of Christoffel Symbols

$(∇XY)k=Xi(∇iY)k=Xi(∂Yk∂xi+ΓimkYm)$

Standard Deviation

$σ=1N∑i=1N(xi−μ)2.$
Solving the quadratic equation. Suppose a x^2+b x+c=0 and a!=0. We first divide by \a to get x^2+b/a x+c/a=0. Then we complete the square and obtain x^2+b/a x+(b/(2a))^2-(b/(2a))^2+c/a=0. The first three terms factor to give (x+b/(2a))^2=(b^2)/(4a^2)-c/a. Now we take square roots on both sides and get x+b/(2a)=+-sqrt((b^2)/(4a^2)-c/a). Finally we move the b/(2a) to the right and simplify to get the two solutions: x_(1,2)=(-b+-sqrt(b^2-4a c))/(2a)