How to Use This Text

Here are some suggestions about how you (the student) should use this text. The author, having been a student himself in the distant past, knows quite well how the typical science/engineering student uses a text. Usually, the text is given a quick, superficial read (perhaps "glance" is more accurate) to get acquainted with the "big picture", the location of the key results and equations, etc. The homework problems get assigned and the student reads the text a bit more closely with the pragmatic goal of finding just what is needed to solve the problems. Finally, the text and the problems are frantically reviewed prior to the agony of the periodic exams. If a sufficiently large number of very diverse homework problems (and exams!) could be created and assigned, the usual way of doing things might work out reasonably well. Unfortunately, this "sufficiently large number" of problems to solve is usually too high a number to be practical for the student, for the instructor, and (most importantly) for the author. The best way to understand the material that is presented here is simply to spend time carefully working through it. Some of this will be done for you, at the blackboard, by your instructor. But it will take a super-human instructor to get you to assimilate all that you need to know via the few hours of lecture you get each week. It’s an unpleasant fact, but we learn the most not by listening to well-crafted lectures, but by working things out for ourselves. With that in mind, there are two key tools in the text that will help you along the way.

Exercises: The exercises typically involve providing intermediate steps, arguments, computations, and additional derivations in the various developments. They represent an attempt to help you focus your attention as you work through the material. They should not take much effort and can often times be done in your head. If you are really stumped and/or are filling up your trash can with unsuccessful computations, then you are missing a key elementary fact — get help!
Problems: The problems represent more substantial endeavors than the exercises, although none should be terribly painful. Some problems fill in important steps in the main text, some provide key applications/extensions. Watch out — some problems will assume you are aware of basic math/physics results from other classes.