Here’s le me trying out the MathJax javascript engine on my tumblr, and while I’m pleased with the results so far! 😉 I regret having to notice that equations who start with begin{aligned}, and end with end{aligned}, seem to confuse the script!?
Please consider this post as a “warming up” excerice. A way for me to get comfortably in writing in: (LaTeX). 😉
The Lorenz Equations:
[ begin{aligned} dot{x} & = sigma(y-x) \ dot{y} & = rho x – y – xz \ dot{z} & = -beta z + xy end{aligned} ]
The Cauchy-Schwarz Inequality:
[ left( sum_{k=1}^n a_k b_k right)^2 leq left( sum_{k=1}^n a_k^2 right) left( sum_{k=1}^n b_k^2 right) ]
A Cross product formula:
[ mathbf{V}_1 times mathbf{V}_2 = begin{vmatrix} mathbf{i} & mathbf{j} & mathbf{k} \ frac{partial X}{partial u} & frac{partial Y}{partial u} & 0 \ frac{partial X}{partial v} & frac{partial Y}{partial v} & 0 end{vmatrix} ]
The probability of getting (k) heads when flipping (n) coins is:
[ P(E) = {n choose k} p^k (1-p)^{ n-k} ]
An Identity of Ramanujan:
[ frac{1}{Bigl(sqrt{phi sqrt{5}}-phiBigr) e^{frac25 pi}} = 1+frac{e^{-2pi}} {1+frac{e^{-4pi}} {1+frac{e^{-6pi}} {1+frac{e^{-8pi}} {1+ldots} } } } ]
A Rogers-Ramanujan Identity:
[ 1 + frac{q^2}{(1-q)}+frac{q^6}{(1-q)(1-q^2)}+cdots = prod_{j=0}^{infty}frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, quadquad text{for $|q|<1$}. ]
Maxwell’s Equations:
[ begin{aligned} nabla times vec{mathbf{B}} -, frac1c, frac{partialvec{mathbf{E}}}{partial t} & = frac{4pi}{c}vec{mathbf{j}} \ nabla cdot vec{mathbf{E}} & = 4 pi rho \ nabla times vec{mathbf{E}}, +, frac1c, frac{partialvec{mathbf{B}}}{partial t} & = vec{mathbf{0}} \ nabla cdot vec{mathbf{B}} & = 0 end{aligned} ]
(✿づ◠‿◠)づ
Or: All this without predefined formatting:
The Lorenz Equations:
[
begin{aligned}
dot{x} & = sigma(y-x) \
dot{y} & = rho x - y - xz \
dot{z} & = -beta z + xy
end{aligned}
]
The probability of getting (k) heads when flipping (n) coins is:
[
P(E) = {n choose k} p^k (1-p)^{ n-k}
]
An Identity of Ramanujan:
[
frac{1}{Bigl(sqrt{phi sqrt{5}}-phiBigr) e^{frac25 pi}} =
1+frac{e^{-2pi}} {1+frac{e^{-4pi}} {1+frac{e^{-6pi}}
{1+frac{e^{-8pi}} {1+ldots} } } }
]
A Rogers-Ramanujan Identity:
[
1 + frac{q^2}{(1-q)}+frac{q^6}{(1-q)(1-q^2)}+cdots =
prod_{j=0}^{infty}frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
quadquad text{for $|q|<1$}.
]
Maxwell’s Equations:
[
begin{aligned}
nabla times vec{mathbf{B}} -, frac1c, frac{partialvec{mathbf{E}}}{partial t} & = frac{4pi}{c}vec{mathbf{j}} \
nabla cdot vec{mathbf{E}} & = 4 pi rho \
nabla times vec{mathbf{E}}, +, frac1c, frac{partialvec{mathbf{B}}}{partial t} & = vec{mathbf{0}} \
nabla cdot vec{mathbf{B}} & = 0
end{aligned}
]
Yet another fine blog…. 😅 