These reports are pre-thesis 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.

A shorter report on a particular model of ECIIsc can be found here.


Is 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.
PDF version

Mathieu's Equations

A detailed look at these important equations is found here.
PDF version

Successive (simultaneous) Overrelaxation

A useful presentation on this numerical method is found here.
PDF version

Quantization of the Harmonic Oscillator

Though found in many text books, we present a derivation with more detail than typical here.
PDF version

Quantum Mechanics of Hydrogen

Shown in more detail than typical, the basic equations for the hydrogen atom are derived here.
PDF version

Aufbau Principal and Selection Rules

An incomplete look at Rydberg atoms (to be finished in time) is here.
PDF version

Electronic Shell Periodic Table (2006)

Collected derivation of Stirling's equation

I 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 zero-axis skew symmetric matrix. This is done in the context of a wedge product example and can be found here.
PDF version


Institute for Quantum Information

Society for Neuroscience

Low Temperature Lab @ Drexel

Wolfram Mathworld

Timothy Jones (tdj28 [at]