A Geometric Approach to Differential Forms

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9780817683030: A Geometric Approach to Differential Forms

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.

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"[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 (Review of First Edition)

"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)."                                                                                   ―Mathematical Reviews (Review of First Edition)

The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the advanced undergraduate level.  The author approaches the subject 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. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions.

The second edition includes a completely new chapter on differential geometry, as well as other new sections, new exercises and new examples. Additional solutions to selected exercises have also been included. The work is suitable for use as the primary textbook for a sophomore-level class in vector calculus, as well as for more upper-level courses in differential topology and differential geometry.

About the Author:

David Bachman, Ph.D., is an assistant professor of mathematics at Pitzer College in California. He currently teaches courses in multivariable calculus as well as mathematical logic games.

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Book Description BIRKHAUSER BOSTON INC, United States, 2011. Hardback. Book Condition: New. 2nd ed. 2012. Language: English . Brand New Book. 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. Bookseller Inventory # AAZ9780817683030

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Book Description BIRKHAUSER BOSTON INC, United States, 2011. Hardback. Book Condition: New. 2nd ed. 2012. Language: English . Brand New Book. 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. Bookseller Inventory # AAZ9780817683030

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Book Description Birkh?user, 2011. Book Condition: New. 2011. 2nd ed. 2012. Hardcover. This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. Num Pages: 174 pages, 43 black & white illustrations, biography. BIC Classification: PBKB; PBKS; PBMP. Category: (P) Professional & Vocational. Dimension: 237 x 164 x 17. Weight in Grams: 404. . . . . . . Bookseller Inventory # V9780817683030

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Book Description Birkhäuser. Book Condition: New. 2011. 2nd ed. 2012. Hardcover. This text presents differential forms from a geometric perspective accessible at the undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. Num Pages: 174 pages, 43 black & white illustrations, biography. BIC Classification: PBKB; PBKS; PBMP. Category: (P) Professional & Vocational. Dimension: 237 x 164 x 17. Weight in Grams: 404. . . . . . Books ship from the US and Ireland. Bookseller Inventory # V9780817683030

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