# Differential Forms: Integration on Manifolds and Stokes's Theorem: A Complement to Vector Calculus

## Steven H. Weintraub

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This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods.

* Treats vector calculus using differential forms
* Presents a very concrete introduction to differential forms
* Develops Stokess theorem in an easily understandable way
* Gives well-supported, carefully stated, and thoroughly explained definitions and theorems.
* Provides glimpses of further topics to entice the interested student

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Differential forms are a powerful computational tool used in advanced mathematics. Until this text, multivariable calculus was taught mostly using the outdated notions of vector fields and related matters. Theuse of differential forms unifies the subject and makes it more understandable, so students learning the subject from this book should emerge with a better conceptual understanding of it. * Treats vector calculus using differential forms * Presents a very concrete introduction to differential forms * Develops Stokess theorem in an easily understandable way * Gives well-supported, carefully stated, and thoroughly explained definitions and theorems. * Provides glimpses of further topics to entice the interested student

Steven H. Weintraub is a Professor of Mathematics at Lehigh University. He received his Ph.D. from Princeton University, spent many years at Louisiana State University, and has been at Lehigh since 2001. He has visited UCLA, Rutgers, Oxford, Yale, Gottingen, Bayreuth, and Hannover. Professor Weintraub is a member of the American Mathematical Society and currently serves as an Associate Secretary of the AMS. He has written more than 50 research papers on a wide variety of mathematical subjects, and ten other books.

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