[pdf] A Course in Mathematical Physics II: Classical Field Theory (Course in Mathematical Physics) Walter E. Thirring

Combining the corrected editions of both volumes on classical physics of Thirring’s course in mathematical physics, this treatment of classical dynamical systems employs analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems. Problems discussed in detail include nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses differential geometry to examine both Maxwell’s and Einstein’s equations with new material added on guage theory.