Class Resources

Energy I Recitation

TDEC 111 Recitation

TDEC 115 Recitation

Various Articles

Mach's Principle

PhD Oral qualifying report on Mach's Principle. Unpublished. This paper reviews some of the history of Mach's principle in physiscs and explores some possible experimental consequences of anisotropic intertia.

General Relativity

Critical review of the Cooperstock-Tieu Galaxy model. Unpublished. Reviews the galaxy model propose by Cooperstock and Tieu which seeks to explain the flat rotation curves of galaxies without resorting to dark matter within the context of General Relativity. It is shown that the model is internally inconsistent. This paper is also available on the archive.

Solutions to Wald's General Relativity. Complete problems and solutions. So far only chatpers 2 and 3 are finished.

Cohomology

End of the chapter exercises from Madsen's and Tornhave's "From Calculus to Cohomology". Chapter 1 and 2, Chapter 3, Chapter 4, Chapters 5 and 6, Chapter 7. Sorry for any typos!

Group Theory

Master Analytic Representation for A1 looks at the problem of constructing all of the unitary irreducible representations of the real forms of the root space A1, which corresponds to the complex lie algebra sl(2,c). The real forms are su(2) and su(1,1). All UIR are constructed using an extension of Schwinger's representation of angular momentum.

Ch2 Solutions for R. Gilmore's Lie Groups, Physics, and Geometry.

Electromagnetism

On the Flux Rule looks at the relation between induced EMF and change in flux for circuits in the presence of magnetic fields. The rule is derived from Maxwell's equations using the expression for the time derivative of a surface integral with moving domain. So called exceptions to the flux rule are examined and it is shown that these are actually misapplications of Kirchhoff's law, not a failure of the flux rule itself.

forthcoming: paper describing the solution of the spin-1 wave equation in a rotating coordinate system. Helicity-rotation-coupling effects are evident.

Miscellaneous

On the Relation between Real and Complex Jacobian Determinants. This papers considers how one determines whether a multidimensional complex map has maximal rank, similar to how one would with a real map. Results are obtained using Sylvester's theorem on block determinants.

Elementary solution of the damped harmonic oscillator. This method requires a little bit of complex analysis, but otherwise is at the level of elementary calculus and requires no special machinery.

Derivation of the Doppler shift. The Doppler shift equations are derived exploiting invariance principles in the more general cases, keeping the hard work to a minimum.

Paradoxical Twins: Beyond an Introduction The twin paradox is analyzed in situations where no acceleration is necessary for the twins to reunite. LaTeX Beamer presentation in pdf format. Sorry if the format makes it difficult to understand - I should add a complete article version at some point.

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