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    • Mathematics, Engineering and Computer Science Undergraduate Theses
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    Curves, Vectors, 1-Forms, And Other Forms Expressed In Terms Of Pictorial, Abstract, And Components In Curved Space

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    1975_DuffyJ_THS_0001210.pdf (21.96Mb)
    Author
    Duffy, James
    Advisor
    Noel Bowman; John Semmens; Alfred Murray
    Date of Issue
    1975-04-01
    Metadata
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    URI
    https://scholars.carroll.edu/handle/20.500.12647/3492
    Title
    Curves, Vectors, 1-Forms, And Other Forms Expressed In Terms Of Pictorial, Abstract, And Components In Curved Space
    Type
    thesis
    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.
    Degree Awarded
    Bachelor's
    Semester
    Spring
    Department
    Mathematics, Engineering & Computer Science
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