Differential Forms: Theory and Practice

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 problemsIncludes computational methods to enable the reader to effectively use differential formsIntroduces theoretical concepts in an accessible manner

Differential Forms
The Algrebra of Differential Forms
Exterior Differentiation
The Fundamental Correspondence 
Oriented Manifolds
The Notion Of A Manifold (With Boundary)
Orientation 

Differential Forms Revisited
l-Forms
K-Forms
Push-Forwards And Pull-Backs 

Integration Of Differential Forms Over Oriented Manifolds
The Integral Of A 0-Form Over A Point (Evaluation)
The Integral Of A 1-Form Over A Curve (Line Integrals)
The Integral Of A2-Form Over A Surface (Flux Integrals)
The Integral Of A 3-Form Over A Solid Body (Volume Integrals)
Integration Via Pull-Backs 

The Generalized Stokes' Theorem
Statement Of The Theorem
The Fundamental Theorem Of Calculus And Its Analog For Line Integrals
Green's And Stokes' Theorems
Gauss's Theorem
Proof of the GST 

For The Advanced Reader
Differential Forms In IRN And Poincare's Lemma
Manifolds, Tangent Vectors, And Orientations
The Basics of De Rham Cohomology 

Appendix
Answers To Exercises
Subject Index