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

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Authors
Duffy, James
Advisor
Noel Bowman
John Semmens
Alfred Murray
Editor
Date of Issue
1975-04-01
Subject Keywords
Publisher
Citation
Series/Report No.
item.page.identifier
Title
Curves, Vectors, 1-Forms, And Other Forms Expressed In Terms Of Pictorial, Abstract, And Components In Curved Space
Other Titles
Type
thesis
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.
Sponsors
Degree Awarded
Bachelor's
Semester
Spring
Department
Mathematics, Engineering & Computer Science