Calculating matrix exponentials.

 I wanted to calculate by hand the exponential of a 3x3 matrix so I wrote out examples of two methods of doing this. To see the PDF click on the link below.

https://drive.google.com/file/d/0BxPw8lRke1HBQnd2RzFkNVYtQjA/view?usp=sharing

The kinetics of consecutive reactions.

This post presents the kinetic equation for consecutive chemical reactions of the type:

with irreversible, first order steps. They have rate constants k₁ and k₂ s^-1. Let the concentrations of the reactants be expressed as x_t,  y_t,  z_t  where x_t  is the concentration of x at time t.

The kinetics of the sequence are completely determined by the equation:

 This solution was derived using Williamson’s algorithm as described below
https://drive.google.com/file/d/0BxPw8lRke1HBdmpfQ2hNMFFfVVU/view?usp=sharing.