The elegance of differential forms in vector calculus and electromagnetics

Hdl Handle:
http://hdl.handle.net/10034/345818
Title:
The elegance of differential forms in vector calculus and electromagnetics
Authors:
Parkinson, Christian
Abstract:
In the chapter one of this text we give an introduction to, and discuss the main integral theorems, of vector calculus; Green's theorem, Stokes' theorem and Gauss' Divergence theorem. Note that the main resource used for this chapter is [8]. Chapter two introduces differential forms and exterior calculus; in it we discuss exterior multiplication and exterior differentiation giving proofs for properties of both. We discuss the integration of differential forms in chapter three and provide definitions of the Divergence, Gradient and Curl and main integral theorems of vector calculus including the Generalised Stokes' theorem that encloses them all in terms of such forms. Further we give a proof of the Generalised Stokes', Green's, Stokes' and Gauss' Divergence theorems. Given the elegance of differential forms that enables us to write the integral theorems of vector calculus as one theorem, the Generalised Stokes' theorem, we show a second elegance by deducing and proving Maxwell's equations, whilst reducing them from four equations to just two. Finally we provide some current research involving differential forms.
Advisors:
Roberts, Graham
Publisher:
University of Chester
Publication Date:
Sep-2014
URI:
http://hdl.handle.net/10034/345818
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
Masters Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorRoberts, Grahamen
dc.contributor.authorParkinson, Christianen
dc.date.accessioned2015-03-02T11:39:43Zen
dc.date.available2015-03-02T11:39:43Zen
dc.date.issued2014-09en
dc.identifier.urihttp://hdl.handle.net/10034/345818en
dc.description.abstractIn the chapter one of this text we give an introduction to, and discuss the main integral theorems, of vector calculus; Green's theorem, Stokes' theorem and Gauss' Divergence theorem. Note that the main resource used for this chapter is [8]. Chapter two introduces differential forms and exterior calculus; in it we discuss exterior multiplication and exterior differentiation giving proofs for properties of both. We discuss the integration of differential forms in chapter three and provide definitions of the Divergence, Gradient and Curl and main integral theorems of vector calculus including the Generalised Stokes' theorem that encloses them all in terms of such forms. Further we give a proof of the Generalised Stokes', Green's, Stokes' and Gauss' Divergence theorems. Given the elegance of differential forms that enables us to write the integral theorems of vector calculus as one theorem, the Generalised Stokes' theorem, we show a second elegance by deducing and proving Maxwell's equations, whilst reducing them from four equations to just two. Finally we provide some current research involving differential forms.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.subjectvector calculusen
dc.subjectelectromagneticsen
dc.titleThe elegance of differential forms in vector calculus and electromagneticsen
dc.typeThesis or dissertationen
dc.type.qualificationnameMScen
dc.type.qualificationlevelMasters Degreeen
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