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Vector
Calculus
Michael Corral
Vector Calculus
Michael Corral
Schoolcraft College
About the author:
Michael Corral is an Adjunct Faculty member of the Department of Mathematics
at Schoolcraft College. He received a . in Mathematics from the University
of California at Berkeley, and received an . in Mathematics and an . in
Industrial & Operations Engineering from the University of Michigan.
This text was typeset in LATEX 2ε with the KOMA-Script bundle, using the GNU
Emacs text editor on a Fedora Linux system. The graphics were created using
MetaPost, PGF, and Gnuplot.
Copyright
c 2008 Michael Corral.
Permission is granted to copy, distribute and/or modify this document under the terms
of the GNU Free Documentation License, Version or any later version published
by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts,
and no Back-Cover Texts. A copy of the license is included in the section entitled
“GNU Free Documentation License”.
Preface
This book covers calculus in two and three variables. It is suitable for a one-semester
course, normally known as “Vector Calculus”, “Multivariable Calculus”, or simply
“Calculus III”. The prerequisites are the standard courses in single-variable calculus
(. Calculus I and II).
I have tried to be somewhat rigorous about proving results. But while it is impor-
tant for students to see full-blown proofs - since that is how mathematics works - too
much rigor and emphasis on proofs can impede the flow of learning for the vast ma-
jority of the audience at this level. If I were to rate the level of rigor in the book on a
scale of 1 to 10, with 1 pletely informal and 10 pletely rigorous, I
would rate it as a 5.
There are 420 exercises throughout the text, which in my experience are more than
enough for a semester course in this subject. There are exercises at the e