# LaTeX Demo Page

## TeX Notation

When a0a≠0, there are two solutions to ax2+bx+c=0ax2+bx+c=0 and they are

x=b±b24ac2a.x=−b±b2−4ac2a.

## The Lorenz Equations

x˙=σ(yx)y˙=ρxyxzz˙=βz+xyx˙=σ(y−x)y˙=ρx−y−xzz˙=−βz+xy

## The Cauchy-Schwarz Inequality

(k=1nakbk)2(k=1na2k)(k=1nb2k)(∑k=1nakbk)2≤(∑k=1nak2)(∑k=1nbk2)

## A Cross Product Formula

V1×V2=ijk XuYu0 XvYv0 V1×V2=|ijk ∂X∂u∂Y∂u0 ∂X∂v∂Y∂v0 |

## The probability of getting kk heads when flipping nn coins is:

P(E)=(nk)pk(1p)nkP(E)=(nk)pk(1−p)n−k

## An Identity of Ramanujan

1(ϕ5ϕ)e25π=1+e2π1+e4π1+e6π1+e8π1+1(ϕ5−ϕ)e25π=1+e−2π1+e−4π1+e−6π1+e−8π1+…

## A Rogers-Ramanujan Identity

1+q2(1q)+q6(1q)(1q2)+=j=01(1q5j+2)(1q5j+3),for |q|<1.1+q2(1−q)+q6(1−q)(1−q2)+⋯=∏j=0∞1(1−q5j+2)(1−q5j+3),for |q|<1.

## Maxwell's Equations

×B⃗ 1cE⃗ t=4πcj⃗ E⃗ =4πρ×E⃗ +1cB⃗ t=0⃗ B⃗ =0∇×B→−1c∂E→∂t=4πcj→∇⋅E→=4πρ∇×E→+1c∂B→∂t=0→∇⋅B→=0

## In-line Mathematics

Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression 3x1+(1+x)23x−1+(1+x)2 is an example of an inline equation. As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.