Lectures: Tuesdays and Thursdays 11:20 AM -- 12:40 PM in the Math Tower, P-131.

Instructors: Jerry Jenquin and William D. Linch III.

Office Hours: Jerry's are 10 -- 11 AM on Tuesdays and Thursdays.
William's are 1:30 -- 2:30 PM on Tuesdays and Thursdays.

Suggested Prerequisites We'll be assuming familiarity with the material covered in MAT 530 and 531. Some previous exposure to physics, while helpful, is by no means necessary.

Course Content: In this first semester we will cover Classical Newtonian Mechanics, Classical Relativistic Mechanics, and Electromagnetism. Specifically we hope to cover the following:

Classical Newtonian Mechanics

Paths in Euclidean space and Newton's 2nd Law.
Phase space and symplectic geometry.
Hamiltonian mechanics in the Newtonian setting.
Variational principles, Lagrangian mechanics.
Symmetry and Noether's theorem.
The Euclidean group, symmetry, and conserved charges (a.k.a. Newtonian kinematics).
Time translation, energy, and dynamics.
Hamiltonian mechanics from Lagrangian mechanics.
Gravitational potentials and solvable systems.

Classical Relativistic Mechanics

Geometry on Minkowski space.
Lagrangian for paths on Minkowski space.
The Poincare group, symmetry, and relativistic kinematics.
Reparameterization invariance.

Electromagnetism

Differential forms, Stoke's theorem, currents, flows.
Hodge star for Euclidean, Lorentzian signatures and duality.
Electromagnetic fields and Maxwell's equations
PDE's on Minkowski space and Poincare symmetry
Laplace and wave equations, Green's operators, boundary conditions
Exact solutions: propagating waves, monopoles, instantons, ...
Lagrangian formulation of electromagnetism
Hamiltonian theory of electromagnetism
Gauge symmetry and connections on principal R-bundles
Magnetic sources, Dirac charge quantization, and principal U(1)-bundles
Generalizations in various directions.

Texts and Online Notes: Although there are no official texts for this course here's a list of references for some of the topics we'll be covering and some of the prerequisite topics. In particular we recommend the following texts to complement the lectures.

Mathematical Methods of Classical Mechanics by V.I. Arnold.
A Course in Mathematics for Students of Physics by Paul Bamberg and Shlomo Sternberg.
Overview of Selected Topics in Physics by William D. Linch III. These notes offer a treatment closer to what one would find in a physics text. It's a work in progress.

We are also fortunate to have Gabriel Drummond-Cole's TeX'd course notes, annotated with physics commentary by William.

Homework: We will provide several problem sets throughout the semester. The best way to learn the material is to attempt these problems and even come up with and solve some problems on your own.

Grades: Throughout the semester students will be expected to present homework solutions in class. The course grade will be determined solely by these presentations.

DSS advisory: If you have a physical, psychiatric, medical, or learning disability that could adversely affect your ability to carry out assigned course work, we urge you to contact the Disabled Student Services office (DSS), Educational Communications Center (ECC) Building, room 128, (631) 632-6748..