 Now we consider the momentum equation for normal and tangential to shock.For formula_8- component, 

Second term of L.H.S and first term of R.H.S are zero due to assumption (2) and (1) respectively.Then,

Or using continuity,

Expanding and simplifying [Using the facts that, to the first order, in the limit as formula_12, formula_13 and formula_14], we obtain

We skip the analysis of the formula_19-component of the momentum and move on to the first law of thermodynamics, which is

First term of L.H.S,next three terms of L.H.S and first term of R.H.S are zero due to assumption (3),(4) and (1) respectively.