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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 have completed 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