dc.contributor.advisor Roberts, Graham en dc.contributor.author Parkinson, Christian * dc.date.accessioned 2015-03-02T11:39:43Z en dc.date.available 2015-03-02T11:39:43Z en dc.date.issued 2014-09 en dc.identifier.uri http://hdl.handle.net/10034/345818 en dc.description.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. dc.language.iso en en dc.publisher University of Chester en dc.subject vector calculus en dc.subject electromagnetics en dc.title The elegance of differential forms in vector calculus and electromagnetics en dc.type Thesis or dissertation en dc.type.qualificationname MSc en dc.type.qualificationlevel Masters Degree en refterms.dateFOA 2018-08-13T21:53:01Z html.description.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.
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