Preface
In writing this Solution Manual I have learned a very important lesson. As a
student, I thought that the best way to master a subject was to go to a superb
university and study with an established expert. Later, I realized instead that the
best way was to teach a course on the subject. Yet later, I was convinced that the
best way was to write a detailed and extensive textbook. Now I know that all these
years I have been wrong: in fact the best way to master a subject is to write the
Solution Manual.
In solving the problems for this Manual I have been forced to confront myriad
technical details that might have tripped up the unsuspecting student. Students and
teachers can thank me for simplifying or screening out problems that required pages of
unenlightening calculations. Occasionally I had to go back to the text and delete the
word “easily” from problem references that read “it can easily be shown (Problem ...).”
Throughout, I have tried to choose data or problem conditions that are particularly
instructive. In solving these problems, I have found errors in early drafts of this text
(as well as errors in books by other authors and even in classic refereed papers), and
thus the accompanying text has been improved for the writing of this Manual.
I have tried to make the problem solutions self-contained and self-explanatory. I
have gone to great lengths to ensure that the solutions are correct and clearly presented
— many have been reviewed by students in several classes. Surely there are errors and
typos in this manuscript, but rather than editing and rechecking these solutions over
months or even years, I thought it best to distribute the Manual, however flawed,
as early as possible. I accept responsibility for these inevitable errors, and humbly
ask anyone finding them to contact me directly. (Please, however, do not ask me to
explain a solution or help you solve a problem!) It should be a small matter to change
the Manual for future printings, and you should contact the publisher to check that
you have the most recent version. Notice, too, that this Manual contains a list of
known typos and errata in the text which you might wish to photocopy and distribute
to students.
I have tried to be thorough in order to help students, even to the occassional fault of
verbosity. You will notice that several problems have the simple “explain your answer
in words” and “graph your results.” These were added for students to gain intuition
and a deeper understanding. Graphing per se is hardly an intellectual challenge, but
if the student graphs functions, he or she will develop intuition and remember the
problem and its results better. Furthermore, when the student later sees graphs of
data from dissertation or research work, the link to the homework problem and the
material in the text will be more readily apparent. Note that due to the vagaries
of automatic typesetting, figures may appear on pages after their reference in this
Manual; be sure to consult the full solution to any problem.
I have also included worked examples and so sample final exams with solutions to
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