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https://library.biblioboard.com/viewer/e1e754c3-12e4-4981-b15c-e05bfb57ada9/45

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https://www.youtube.com/watch?v=TJAQNlGvfjE&list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6&index=5

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https://www.youtube.com/watch?v=dtvM-CzNe50&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=10

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https://www.youtube.com/watch?v=d5da-mcVJ20&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=9

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Vectors components are measured by counting how many are used to construct a vector

Convector Components are measured by counting the number of lines the covector pierces.

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Thus e i and epilon i are in the same directions in their respective vector spaces.

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https://www.youtube.com/watch?v=uPbBDToXjBw&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=5

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https://www.youtube.com/watch?v=rG2q77qunSw&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=8

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https://www.youtube.com/watch?v=LNoQ_Q5JQMY&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=7

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https://www.youtube.com/watch?v=ipRrCPvftTk&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=4

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https://www.youtube.com/watch?v=SfOiOPuS2_U&t=942s

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Christoffel Symbols and
Second Fundamental Form Coefficients

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Christoffel Symbols Using Einstein Notation

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Christoffel Symbols Using Einstein Notation

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summing over K = 1 to 2

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of second order derivative of R in respect to U and V

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of second order derivative of R in respect to U and V

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expressed in u and V coordinates

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Christoffel Symbols & 2nd Fundamental Form

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Christoffel Symbols & 2nd Fundamental Form

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Coefficients for a linear combination using the new basis vectors

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It would be nice if messy equations could be  re written as nice equations. So one can  create a nice form and the work backwards to assign the messy components to the nicer ones. Christoffel symbols are part of the nice forms that hide the messiness.

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https://www.youtube.com/watch?v=1CuTNveXJRc

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https://www.youtube.com/watch?v=Af9JUiQtV1k&t=67s

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Used as coefficients to write linear combination to express derivative of the Basis vectors

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These are notes of mine for reference as I watch these videos. See links for the actual videos.