文档介绍：A Geometric Approach to Differential
Forms
David Bachman
California Polytechnic State University
E-mail address: ******@
For the Instructor
The present work is not meant to contain any new material about differential
forms. There are many good books out there which give nice, complete treatments of
the subject. Rather, the goal here is to make the topic of differential forms accessible
to the sophomore level undergraduate. The target audience for this material is
primarily students who pleted three semesters of calculus, although the
later sections will be of interest to advanced undergraduate and beginning graduate
students. At many institutions a course in linear algebra is not a prerequisite for
vector calculus. Consequently, these notes have been written so that the earlier
chapters do not require many concepts from linear algebra.
What follows began as a set of lecture notes from an introductory course in
differential forms, given at Portland State University, during the summer of 2000.
The notes were then revised for subsequent courses on multivariable calculus and
vector calculus at California Polytechnic State University. At some undetermined
point in the future this may turn into a full scale textbook, so any feedback would
be greatly appreciated!
I thank several people. First and foremost, I am grateful to all those students
who survived the earlier versions of this book. I would also like to thank several of
my colleagues for giving me ments. Most notably, Don Hartig had several
comments after using an earlier version of this text for a vector calculus course. John
Etnyre and Danny Calegari gave me feedback regarding Chapter 6. Alvin Bachman
had good suggestions regarding the format of this text. Finally, the idea to write this
text came from conversations with Robert Ghrist while I was a graduate student at
the University of Texas at Austin. He also deserves my gratitude.
Prerequisites. Most of the text is writt