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Can someone suggest me a list of book or workbook with examples and solutions on differential forms and double improper integral?

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Advanced Calculus: A Differential Forms Approach by Harold Edwards is a good introductory level explanation of the material with lots of examples.

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Weintraub's Differential Forms: A Complement to Vector Calculus is an elementary text contains many examples of integrating differential forms and has answers to all exercises. There are many errata in the text however and it would be a good idea to get an updated list from the author's website before reading.

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This book has lots of good basic exercises of the sort I think the OP is asking for. – Robert Haraway Mar 3 '12 at 20:53

I recommend Vector Calculus, Linear Algebra, and Differential Forms by Hubbard & Hubbard. Not only does it cover differential forms, it also integrates the study of linear algebra and multivariable calculus.

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