This introductory text explores the essentials of partial differential equations applied to common problems in engineering and the physical sciences. It reviews calculus and ordinary differential equations, explores integral curves an surfaces of vector fields, the Cauchy-Kovalevsky theory and more. Includes problems and answers.
A superb introduction to the topic. This book is particularly well-suited to math majors, and is organized in a somewhat unorthodox manner; starting with first order linear and quasi-linear systems after a review of mulitvariable calculus, instead of the normal second order equations.
Picked this up to go along with our gauche, everything-wrong-with-American-math-education, "with media applications!" $80 hardback piece of doggerel for DiffEQ freshman year. Unfortunately, this is of the everything-wrong-with-anonymous-Eastern-European-publishing-as-bought-for-pennies-on-the-Bulgarian-lev-by-Dover school. Between the two, I'm unsure how I ever managed an A in MATH 2403, except that it was a stupidly easy summer instance.
Man, I used to be able to do any calculus problem I looked at, in my head, largely instantaneously. I can't do that anymore :/. On the other hand, over the years I've gotten better at counting very quickly and Applied Gambling, which I suppose is more applicable to my current work.