W. E. Williams.
Partial Differential Equations.
OUP. 1980
Partial differential equations are an important part of
final-year undergraduate work in the mathematical sciences.
Students should gain an understanding of the principles from this course text,
which has an “applied” approach and numerous worked examples.
They should then be in a position to apply their knowledge in unfamiliar situations.
First- and second-order partial differential equations are introduced, with shock waves and “weak” solutions discussed. Elliptic, hyperbolic, and parabolic equations are all treated by Green’s functions, then separation of variables, Fourier series, and transform methods are illustrated. The uses of numerical variational, and perturbation methods are outlined.