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[tex]D_{n}(E)=\frac{Ω}{(2\pi)^{3}}\int_{BZ}dk\delta[E-\epsilon_{n}(k)][/tex] (1)

On the other hand, another formula of DOS is often mentioned as follows,

[tex]D_{n}(E)=\frac{Ω}{(2\pi)^{3}}\int_{S}\frac{dS}{\nabla_{k}E(k)} [/tex] (2)

But,how to derive the first formula in a simple and accesible way ?

Another question is how to derive the second formula according to the first one ?