Analytical and Statistical Mechanics

Description

This course provides an advanced treatment of two key areas covering much of mechanics, specifically the motion of macroscopic systems (rigid bodies, springs, planets etc.), and the behaviour of collections of microscopic particles. Analytical mechanics is a collection of advanced formalisms for classical mechanics, describing the kinematics and dynamics of rigid bodies and systems. Teaching covers planetary motion, rotational dynamics, Lagrange's and Hamilton's equations. This provides the mathematical framework for dealing with systems with many degrees of freedom, and links to the Hamiltonian in quantum mechanics. Building on this, and on elementary knowledge of thermodynamics, the latter part of the course will introduce statistical mechanics. This can give an understanding of real substances, vital in the fields of nanoscience, nanotechnology, materials science and atomic/molecular physics. It covers topics including: the relationship between microscopic structure and thermodynamic properties: microcanonical, canonical and grand ensembles; entropy; chemical potential; equipartition; Fermi-Dirac and Bose-Einstein statistics, ideal classical and quantal gases.. Prior assumed: Calculus II (2205NSC). Co-assumed: Linear Algebra and Applications (2201NSC).