This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Review

From the reviews: "[The author's] idea is to use geometric intuition to alleviate some of the algebraic difficulties...The emphasis is on understanding rather than on detailed derivations and proofs. This is definitely the right approach in a course at this level." —MAA Reviews "This book is intended as an elementary introduction to the notion of differential forms, written at an undergraduate level. ... The book certainly has its merits and is very nicely illustrated ... . It should be noted that the material, which has been tested already in the classroom, aims at three potential course tracks: a course in multivariable calculus, a course in vector calculus and a course for more advanced undergraduates (and beginning graduates)." —Frans Cantrijn, Mathematical Reviews, Issue 2007 d "Students! Read this book if you want to get acquainted with differential forms! This is a kind of unusual book, which is really nice to read for a beginner ... a lot of examples and numerous meaningful ‘experiments’ to get the real meaning behind the scenes, that otherwise should be digged from formal proofs. ... I recommend the book not only for students, but also for teachers!" (�rp�d Kurusa, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

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