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Browsing, as is my wont, in a used bookstore the other day, I serendipitously stumbled across a copy of Steven Krantz's Differential Equations Demystified. I've looked at innumerable books on ODEs and PDEs over the years, so I opened the covers of this one with a sense of jaded deja vu, prompted only by the consideration that I've been impressed by other Krantz books. This book is different from the others. It's ideally suited to finance and economics types who've taken a semester or two of calculus and want a quick intro to ODEs and a taste of PDEs. It has many of the usual topics -- linear ODEs with constant coefficients, method of undetermined coefficients, variation of parameters, power series solutions, Laplace transform, Runge-Kutta methods -- and also a chapter on PDEs and boundary-value problems. Some Amazon reviewers have been grumbling that it doesn't have existence and uniqueness theorems, method of successivbe approximations, and so on. But the inclusion of such would defeat the purpose of the book, which is to provide a rough-and-ready introduction to very basic topics. For those who've already taken courses in ODEs and PDEs, this book is a complete waste of time. But for economics and finance types, whose calc foundations may be a bit shaky, this tome is definitely worth looking at. It's ideal for self-study and can be completed in 4-6 weeks.
