REPORTSThese reports are prethesis studies related to various research projects and courses taken. More recent work can be found in the thesis. 
Mathematics of Neuroscience
Neurons can be described using nonlinear dynamical techniques.
A compilation of my homework reports and final report for a
class I took at Drexel (Math 723) with Dr. Medvedev can be
found here. A number of MATLAB,
C++, and Maple programs for dynamical computations are included.

DecoherenceIs Quantum Decoherence the von Neumann wave collapse? An oral qualifier report can be read here. PDF version 
Master Equation
A detailed derivation of the quantum optics master equation
collected from many sources
and including steps not often found elsewhere is found
here. 
Mathieu's Equations
A detailed look at these important equations
is found here. 
Successive (simultaneous) Overrelaxation
A useful presentation on this numerical method is found
here. 
Quantization of the Harmonic Oscillator
Though found in many text books, we present a derivation with
more detail than typical
here. 
Quantum Mechanics of Hydrogen
Shown in more detail than typical, the basic
equations for the hydrogen atom are derived
here.

Aufbau Principal and Selection Rules
An incomplete look at Rydberg atoms (to be finished in time) is
here. 
Electronic Shell Periodic Table (2006) 
Collected derivation of Stirling's equationI had trouble finding a derivation of Stirling's equation that was thorough and collected, so I ran through some of my text books and collected a cogent single stranded derivation here. 
The Pfaffian and the Wedge Product
Via proofs from Thomas Muir and S. Parameswaran, we remind the reader
of the relationship between the Pfaffian and Determinant for for a
zeroaxis skew symmetric matrix. This is done in the context of a
wedge product example and can be found
here.
