Heat-equation

I, too, took the full-year course with Prof. Holland while he was editing the book. I also took a graduate Complex Analysis course with him a year later. It is no coincidence that it is in these areas - orthogonal functions, PDE solutions in various coordinate sustems, and complex analysis - in which I consider myself an expert to this day.

Prof. Holland teaching style is mirrored in this book. The problems are numerous. He stresses the same key points throught the chapters. You practice, and you are continually reminded. If you have had the priviledge to be taught by Prof. Holland, and you keep up, you must retain the information.

What amazes me to this day is that the famous Prof. Richard Feynman avoided teaching this material to his undergraduates at Caltech. (See his Lectures in Physics, III.) Yet, Prof. Holland managed to teach this to a bunch of sophomores and juniors at the Univ. of Massachusetts to a very high degree of success by knowing what was inportant in physics, and what could be saved for later.

This text cannot be recommended highly enough.

I had the pleasure (challenge?) of taking Prof Holland's one year sequence of courses on Hilbert Space theory at the University of Massachusetts while he was editing this book. I agree with the previous review that the flow of the text, the problems and the descriptions of the concepts are well thought out and enabled me to grasp a rather difficult concept. The two main applications given in the text are heat transfer and, of course, Schroedinger's equation. In the case of heat transfer for instance, a number of different boundary conditions are presented to the student along with different geometries and analysis (Bessel, Fourier, etc).

If you like the problems in the text I can assure you that I crunched through all of them personally!

It's unusual for a book on this topic to be targeted at undergraduates. What's even more unusual is that the author succeeds in explaining differential operators at this level. I found the discussions on the Legendre and Hermite operators especially illuminating. There are numerous worked examples and exercises. The real accomplishment of this text is that the author has managed to select results that are of crucial importance, omitting some important theorems along the way, but maintaining the core idea. That is a difficult trick.