Articles on Differential Forms, Including - Stokes' Theorem, Exterior Derivative, Differential Form, de Rham Cohomology, Exterior Algebra, Hodge Dual, One-Form, Closed and Exact Differential Forms, Two-Form, Volume Form, Interior Product (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Hephaestus Books represents a new publishing paradigm, allowing disparate content sources to be curated into cohesive, relevant, and informative books. To date, this content has been curated from Wikipedia articles and images under Creative Commons licensing, although as Hephaestus Books continues to increase in scope and dimension, more licensed and public domain content is being added. We believe books such as this represent a new and exciting lexicon in the sharing of human knowledge. This particular book is a collaboration focused on Differential forms.More info: In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better definition for integrands in calculus. For instance, ƒ(x) dx is a 1-form which can be integrated over an interval a, b] in the domain of ƒ \int_a DEGREESb f(x)\, dx and similarly ƒ(x, y) dx + g(x, y) dy is a 1-form which has a line integral over any oriented curve γ in the domain of ƒ and g: \int_\gamma f(x, y)\, dx + g(x, y)\, dy. Likewise, a 3-form ƒ(x, y, z) dx dy dz represents something that can be integrated over a region of space. The modern notion of differential forms was pioneered by lie Cartan, and has many applications, especially in geometry, topology and physics.