Dr. Gabriel Williams Assistant Professor Office: RHS 333 Phone: 843.953.0278 Email: williamsgj@cofc.edu Home Curriculum Vitae Research QuickStudy Tools CofC Webpage Physics Department Meteorology Program Weather Analysis Links |
## - QuickStudy Tools-As a professor, I know that there are a number of important topics that are not covered within the standard undergraduate 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/meteorology.## -For Physics Students-Applied Mathematics
Any student who desires to pursue graduate study in physics must be mathematically competent. Most of the notes below are taken from the textbook Mathematical Methods for Physicists by Arfken and Weber. Students should thoroughly go through these notes before graduation. It is assumed that the student has taken (or is currently taken) ordinary differential equations (MATH 320) and is comfortable with vector calculus.
Elementary Probability Theory Tensor Analysis Complex Analysis Differential Equations Sturm-Liouville Theory Gamma Function Legendre Function Bessel Function Hermite Function Fourier Series Fourier and Laplace Transforms Classical Mechanics
It is assumed that the student has taken (or is currently taking) classical mechanics (PHYS 301) and is comfortable with matrix analysis. The following notes are largely taken from Prof. Frank L. H. Wolfs from the University of Rochester. Coupled Oscillations Hamiltonian Minkowski Spacetime Nonlinear Chaos Relativistic Mechanics Scattering Theory 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 Waves Poynting Theorem Maxwell Stress Tensor Electromagnetic Radiation Gauge Theory Helmholtz Theorem Relativity and Electromagnetism 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. Thermodynamics of Blackbody Radiation The Physics of Superfluid Helium Bose-Einstein Distribution Fermi-Dirac Distribution Legendre Transformation Thermoelectric Effect ## -For Meteorology Students-Survey of Meteorology
For all students desiring to obtain the Operational Meteorology concentration, there are two online sources that you should thoroughly go through before you graduate. 1. Practical Meteorology by Roland Stull is an excellent algebra-based survey of atmospheric science presented at the 100- level. This textbook is a companion book to PHYS 105 and should be used as you walk through your 100/200 level courses. 2. Atmospheric Science by Wallace and Hobbs presents a survey of the major topics of atmospheric science at the 300/400 level. This book should be thoroughly used in PHYS 225 and all of your 300/400 level courses. Quasi-Geostrophic (QG) Theory
It is assumed that the student has taken (or is currently taking) synoptic meteorology (PHYS 215) and is comfortable with vector calculus. QG Theory and Prediction Equations of QG Theory Q-Vectors Cyclone Development in QG Theory Application of Petterssen-Sutcliffe Development Theory Frontal Development in QG Theory Isentropic Potential Vorticity (IPV)
It is assumed that the student has taken (or is currently taking) synoptic meteorology (PHYS 215) and is comfortable with vector calculus. Isentropic Analysis Introduction to Isentropic IPV IPV Anomaly Structures and Impacts Impacts of Diabatic Heating and Friction upon IPV Cyclone Development from an IPV Perspective Numerical Weather Prediction (NWP)
It is assumed that the student has taken (or is currently taking) synoptic meteorology (PHYS 215) and is comfortable with vector calculus. To use the links below, you must register with the UCAR COMET program. Introduction to NWP Effective Use of NWP in the Forecast Process: Introduction Gridded Products in the NWS National Blend of Global Models How Mesoscale Models Work Introduction to Ensemble Forecasting Systems NWP Model Fundamentals Adding Value to NWP Guidance |