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Ch 7 logic flow idea

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Phil's brief working note dated 4.6.15, part of the May 2015 update files for his curvilinear systems tensor document. It lists what sections 7.4 to 7.9 should cover, including translations of scalars, vectors and matrices, contraction, the transformation matrices R and S, the metric g raising and lowering indices, and epsilon and delta. It flags sections as too short and ends by deciding to assemble a new Chapter 7 from pieces.

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Chapter 7 Logic Flow PhL 4.6.15 7.4 Prelim translations: how to translate scalar, vector, matrices like M and g and g-1 how g converts vector from one kind to the other single symbol stands for both kinds of vectors how ds2 translates 7.5 Definition of contraction, but no explanation. Section is way too short! 7.6 Dealing with matrix R reason that Rik → Rik V'a = RabVb → V'a = RabVb 7.7 Same for S, way too short for a section! (∂xi/∂x'k) → (∂xi/∂x'k) Sik ≡ (∂xi/∂x'k) → Sik ≡ (∂xi/∂x'k) 'a = STabb = Sba b → V'a = SbaVb // covariant (7.7.1) 7.8 About ε and δ. state the line gab = gab = gba = gba = δa,b without proof because have not done this yet. determinant formula cross product formula 7.9 More translations (a) detR and detS (b) inverse or R and S (c) g raises and lowers ANY index how rank-2 tensor M transforms with ALL index positions. STOP. Instead, I will assemble a new Chapter 7 by grabbing pieces.