Dr. Gabriel Williams
Assistant Professor
Office: JC Long 223
Phone: 843.953.0278
Email: williamsgj@cofc.edu

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Gabriel J. Williams

- QuickStudy Tools-

As a professor, I know that there are a number of topics within mathematics, physics, and atmospheric science that are important, but are usually not covered within the standard core curriculum. This webpage provides an introduction to various topics of relevance for students who are interested in advanced study in physics and/or atmospheric science.

1. Classical Mechanics

It is assumed that the student has taken (or is currently taking) classical mechanics (PHYS 301) and is comfortable with matrix analysis.

Coupled Oscillations
Hamiltonian
Minkowski Spacetime
Nonlinear Chaos
Relativistic Mechanics
Scattering Theory

2. Electromagnetism

It is assumed that the student has taken (or is currently taking) electricity and magnetism (PHYS 409) and is comfortable with vector calculus and ordinary differential equations.

AC Circuits
Electromagnetic Radiation
Electromagnetic Waves
Gauge Theory
Helmholtz Theorem
Legendre Function
Maxwell Stress Tensor
Poynting Theorem
Poynting Vector
Relativity and Electromagnetism

3. Thermal Physics

It is assumed that the student has taken (or is currently taking) thermal physics (PHYS 405) and is comfortable with vector calculus and ordinary differential equations.

Blackbody Radiation
Bose-Einstein Distribution
Fermi-Dirac Distribution
Legendre Transformation
Thermoelectric Effect

4. Applied Mathematics

It is assumed that the student has taken (or is currently taken) ordinary differential equations (MATH 320) and is comfortable with vector calculus.

Bessel Function
Complex Analysis
Differential Equations
Fourier Series
Gamma Function
Hermite Function
Integral Transforms
Sturm-Liouville Theory
Tensor Analysis

updated: 22 August 2017