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

 carrollscholars.legacy.contextkey 12832819 carrollscholars.legacy.itemurl https://scholars.carroll.edu/mathengcompsci_theses/116 carrollscholars.object.degree Bachelor's carrollscholars.object.department Mathematics, Engineering & Computer Science carrollscholars.object.disciplines Algebraic Geometry; Applied Mathematics; Geometry and Topology; Mathematics; Physics carrollscholars.object.season Spring dc.contributor.advisor Noel Bowman dc.contributor.advisor John Semmens dc.contributor.advisor Alfred Murray dc.contributor.author Duffy, James dc.date.accessioned 2020-04-30T10:08:44Z dc.date.available 2020-04-30T10:08:44Z dc.date.embargo 12/31/1899 0:00 dc.date.issued 1975-04-01 dc.description.abstract In 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.uri https://scholars.carroll.edu/handle/20.500.12647/3492 dc.title Curves, Vectors, 1-Forms, And Other Forms Expressed In Terms Of Pictorial, Abstract, And Components In Curved Space dc.type thesis
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