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

Includes bibliographical references.

The General Theory for One First-Order Equation -- The General Theory for One First-Order Equation (Continued) -- Huygens’ Principle in the Theory of Wave Propagation -- The Vibrating String (d’Alembert’s Method) -- The Fourier Method (for the Vibrating String)

Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the wave equation, although the heat equation and the Korteweg-de Vries equation are also discussed. Physical intuition is emphasized. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging!