Rhee H.-K., Aris R., Amundson N.R. First-Order Partial Differential Equations, Volume 1: Theory and Applications of Single Equations

New York: Dover Publications, 1985. — 555 p.This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of most sections. This volume is geared to advanced undergraduates or first-year grad students with a sound understanding of calculus and elementary ordinary differential equations.189 black-and-white illustrations. Author and subject indices.