Hopf L. Introduction to the Differential Equations of Physics

Dover, 1948. - 154 pages. ISBN: B000OLSBRYThe first portion of this concise introduction to ordinary and partial differential equations acquaints the reader with equations describing the more important theories of classical physics. It covers the mechanics of particles, potential, heat conduction, energy, electrodynamics, oscillations, electromagnetic waves and potentials.
The concluding chapters introduce some of the standard ways for solving those differential equations which have been derived: Eigenfunctions, Fourier series and integrals, Green's theorem, particular solutions in coordinates, asymptotic expansions, change of variables, conformal mapping, singularities, and transition to integral equations.
Mathematics is developed in close connection with physical problems, as needed. Elementary physical intuition is skillfully blended with formal mathematics. This volume is specially apt for self-study, since no mathematical background beyond elementary calculus is required of the reader.