Differential Forms: A Complement to Vector Calculus

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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

Audience: Undergraduate math majors and engineering majors through graduate level; anyone who uses calculus regularly.

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques.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

Booknews

Primarily addressed to students in a third-semester, multivariable calculus course who are studying vector calculus, but also of interest to more advanced students who want a concrete introduction to differential forms. Differential forms are explained from the mathematical perspective rather than from that of physics or engineering, as is usually the case. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Steven H. Weintraub is a Professor of Mathematics at Louisiana State University. He received his Ph.D. from Princeton University, and has been at LSU since that time, with temporary leaves to UCLA, Rutgers, Oxford, Yale, Gottingen, Bayreuth, and Hannover (Germany).Professor Weintraub is a member of the American Mathematical Society and a former member of the Council of the AMS. He has written more than 40 research papers and two other books: a graduate algebra book and a reserach monograph.