Covariant and contravariant components, the metric tensor

This blog gives an elementary explanation of the terms covariant and contravariant as applied to vectors and describes how vectors transform under a change of coordinates. The notions of metric tensor and metric equation are explained.

For more information, open the link below.



https://drive.google.com/file/d/0BxPw8lRke1HBdzhGeHU1RkloSzQ/view?usp=sharing

The kinetics of three-stage, successive, first-order reactions.

By Roy Ernest Ballard

2 November 2014

This post is concerned with the kinetics of successive, irreversible, first order reactions. An earlier post on this subject  discussed the kinetics of a two-stage sequence. Here the complete solution is reported for the three-stage sequence:

The solution is:

For more details click the link below.


https://drive.google.com/file/d/0BxPw8lRke1HBUUVlT0RDT3RkQzA/view?usp=sharing

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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.