Curves, Vectors, 1-Forms, And Other Forms Expressed In Terms Of Pictorial, Abstract, And Components In Curved Space

carrollscholars.legacy.contextkey12832819
carrollscholars.legacy.itemurlhttps://scholars.carroll.edu/mathengcompsci_theses/116
carrollscholars.object.degreeBachelor's
carrollscholars.object.departmentMathematics, Engineering & Computer Science
carrollscholars.object.disciplinesAlgebraic Geometry; Applied Mathematics; Geometry and Topology; Mathematics; Physics
carrollscholars.object.seasonSpring
dc.contributor.advisorNoel Bowman
dc.contributor.advisorJohn Semmens
dc.contributor.advisorAlfred Murray
dc.contributor.authorDuffy, James
dc.date.accessioned2020-04-30T10:08:44Z
dc.date.available2020-04-30T10:08:44Z
dc.date.embargo12/31/1899 0:00
dc.date.issued1975-04-01
dc.description.abstractIn this thesis, I will explain old and new views of curves, vectors, 1-forms and tensors. These views will be expressed conceptually in terms of pictorial, abstract and component forms. I will use these techniques to express the idea of both metric and non-metric space and to show relationships between the new and old ideas. I will use the ideas of flat space and demonstrate how they differ from ideas of curved space. In effect, I will show that flat space (the cartesian coordinates) is a special case of curved space by a cancellation of certain terms. The purpose of this thesis is to state why we need curves, vectors, 1-forms and tensors. It will be assumed that the reader has some knowledge of modern algebra, differential equations, modern physics (Lorentz transformations) and some advanced calculus.
dc.identifier.urihttps://scholars.carroll.edu/handle/20.500.12647/3492
dc.titleCurves, Vectors, 1-Forms, And Other Forms Expressed In Terms Of Pictorial, Abstract, And Components In Curved Space
dc.typethesis
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