Some Chapters

Prof. Robert Gilmore Physics Department Email: robert.gilmore@drexel.edu The following set of isolated chapters were written by the author as an antidote for lack of similar presentations that may be readily available elsewhere. Copyright 2004 by Robert Gilmore

[PDF] Dimensional Analysis

Dimensional Analysis is presented in a matrix formulation. The exponents of products of quantities with dimensions are treated as vectors in a linear vector space. Once a choice of basis vectors is made, all exponent vectors can be expressed as linear combinations of the basis vectors. Null vectors describe products of dimensional quantities that are dimension free. Examples are given and include the hydrogen atom, the Planck scales, fluids, and some of the standard dimensionless ratios.

[PDF] Lagrange Multipliers

Lagrange multipliers provide a convenient way to treat constrained optimization problems. This discussion introduces the ideas behind their use and illustrates their use with a large variety of examples.

[PDF] Time-Independent Perturbation Theory

Time independent perturbation theory is formulated in terms of 3 x 3 matrices. The expansion of the eigenvalues and eigenvectors to third order in a smallness parameter is directly generalized to the correct form of perturbation theory to third order for any number of states.

[PDF] Time-Dependent Perturbation Theory

Time-Dependent perturbation theory is formulated in a systematic way in terms of an iterated expansion of the perturbing time-dependent hamiltonian. The expansion is carried out in the spirit of Dyson.

[PDF] The Structure of Thermodynamics

Classical equilibrium thermodynamics is presented in a geometric framework. This provides a useful bookkeeping mechanism for treating the extensive and dual intensive variables. The First Law appears as a differential relation. The Second Law appears as a condition on the curvature of the equilibrium surface. The Third Law is a boundary condition. A simple linear vector space algorithm is presented for computing any thermodynamic partial derivative. The LeChatelier reciprocal relations are derived and stated in simple, elegant form. Fluctuation moments are expressed in terms of the macroscopic static linear susceptibility coefficients. Relaxation of perturbations to the equilibrium surface occur with time constants determined by the kinetic coefficients and the equilibrium susceptibilities. Fluctuation moments and kinetic coefficients are related by the fluctuation-dissipation theorem.

[PDF] Lie Groups: general theory

This summary of the most important aspects of Lie group theory consists of the following sections 1. Introduction 2. Lie Groups 3. Matrix Lie groups 4. Linearization of a Lie Group 5. Matrix Lie algebras 6. Lie algebra tools 7. Structure of Lie algebras 8. Structure of semisimple Lie algebras 9. Root spaces 10. Canonical commutation relations 11. Dynkin diagrams 12. Real forms 13. Riemannian symmetric spaces 14. Summary

[PDF] Quadruply discrete classification for Low Dimensional Chaos