Lectures on partial differential equations / Vladimir I. Arnold ; translated by Roger Cooke.

The general theory for one first-order equation
The general theory for one first-order equation (continued)
Huygen's principle in the theory of wave propagation
The vibrating string (d'Alembert's method)
The Fourier method (for the vibrating string)
The theory of oscillation. The variational principle
The theory of oscillations. The variational principle (continued)
Properties of harmonic functions
The fundamental solution for the Laplacian. Potentials
The double-layer potential
Spherical functions. Maxwell's theorem. The removable singularities theorem
Boundary-value problems for Laplace's equation. Theory of linear equations and systems
The topological content of Maxwell's theorem on the multifield representation of spherical functions.