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PREFACE
General Character and Purpose of the Instructor’s Manual
This Manual contains:
(I) Detailed solutions of the even-numbered problems.
(II) General comments on the purpose of each section and its classroom use, with
mathematical and didactic information on teaching practice and pedagogical aspects. Some
of the comments refer to whole chapters (and are indicated accordingly).
Changes in Problem Sets
The major changes in this edition of the text are listed and explained in the Preface of the
book. They include global improvements produced by updating and streamlining chapters
as well as many local improvements aimed at simplification of the whole text. Speedy
orientation is helped by chapter summaries at the end of each chapter, as in the last edition,
and by the subdivision of sections into subsections with unnumbered headings. Resulting
effects of these changes on the problem sets are as follows.
The problems have been changed. The large total number of more than 4000 problems
has been retained, increasing their overall usefulness by the following:
• Placing more emphasis on modeling and conceptual thinking and less emphasis on
technicalities, to parallel recent and ongoing developments in calculus.
• Balancing by extending problem sets that seemed too short and contracting others
that were too long, adjusting the length to the relative importance of the material
in a section, so that important issues are reflected sufficiently well not only in the
text but also in the problems. Thus, the danger of overemphasizing minor techniques
and ideas is avoided as much as possible.
• Simplification by omitting a small number of very difficult problems that appeared
in the previous edition, retaining the wide spectrum ranging from simple routine
problems to more sophisticated engineering applications, and taking into account the
“algorithmic thinking” that is developing along with computers.
• Amalgamation of text, examples, and problems by including the large number of
more than 600 worked-out examples in the text and by providing problems closely
related to those examples.
• Addition of TEAM PROJECTS, CAS PROJECTS, and WRITING PROJECTS,
whose role is explained in the Preface of the book.
• Addition of CAS EXPERIMENTS, that is, the use of the computer in “experimental
mathematics” for experimentation, discovery, and research, which often produces
unexpected results for open-ended problems, deeper insights, and relations among
practical problems.
These changes in the problem sets will help students in solving problems as well as in
gaining a better understanding of practical aspects in the text. It will also enable instructors
to explain ideas and methods in terms of examples supplementing and illustrating
theoretical discussions—or even replacing some of them if so desired.
“Show the details of your work.”
This request repeatedly stated in the book applies to all the problem sets. Of course, it is
intended to prevent the student from simply producing answers by a CAS instead of trying
to understand the underlying mathematics.
Orientation on Computers
Comments on computer use are included in the Preface of the book. Software systems are
listed in the book at the beginning of Chap. 19 on numeric analysis and at the beginning
of Chap. 24 on probability theory.
ERWIN KREYSZIG
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