Differential Forms: Theory and Practice

ISBN-13: 9780123944030 / Angielski / Twarda / 2014 / 395 str.

Steven H. Weintraub

Opis

Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications. They both unify and simplify results in concrete settings, and allow them to be clearly and effectively generalized to more abstract settings. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems. Differential Forms, 2nd Edition, is a solid resource for students and professionals needing a general understanding of the mathematical theory and to be able to apply that theory into practice.

• Provides a solid theoretical basis of how to develop and apply differential forms to real research problems
• Includes computational methods to enable the reader to effectively use differential forms
• Introduces theoretical concepts in an accessible manner

Recenzje

".a very nice book.covers things at a more leisurely pace, with many examples...would go a long way toward making the subject more popular and accessible." --SIAM Review

"This is a rigorous and well-written treatment of differential forms with a careful and detailed progression from very basic notions." --MAA.org, 24-Sep-14

Spis treści

1. Differential Forms in R n , I 2. Differential Forms in R n , II 3. Push-forwards and Pull-backs in R n 4. Smooth Manifolds 5. Vector Bundles and the Global Point of View 6. Integration of Differential Forms 7. The Generalized Stokes's Theorem 8. de Rham Cohomology

O autorze

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.