An Introduction to Second-Order Partial Differential Equations and the Method of Characteristics

A course book of 30 pages on finding classical solutions to second-order linear PDEs, particularly only covering the method of characteristics as a tool in finding such solutions.

From the start to the end, one only encounters the physical origins of PDEs, classification into hyperbolic, parabolic, and elliptic; characteristic and non‑characteristic curves; and the reductions to canonical form, which allows knowing the nature of the solutions and solving for it when the context calls for basic application of calculus and the theory of ordinary differential equations.

Any reader that comes to this book with the basic knowledge of calculus of several variables and ordinary differential equations would follow its arguments to the end, and be able to classify any second‑order linear PDE, find its characteristic equations, and reduce the PDE to its canonical form. When the canonical form takes a known form, integrate or employ ODE methods to obtain the explicit solution in its general or unique form.