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Spivak Calculus on Manifolds and Epsilon delta proofs
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[QUOTE="unintuit, post: 4958866, member: 529738"] I am currently having some issue understanding, what you may find trivial, epsilon-delta proofs. I have worked through Apostol Vol.1 and ran through Spivak and I found Apostol just uses neighborhoods in proofs instead of the epsilon-delta approach, while nesting neighborhoods is 'acceptable' I would like to correct the weakness of understanding the epsilon-delta approach, to be even more specific I would like to be able to calculate with it and do manipulations. I have found Spivak to be inadequate for teaching this and was hoping you would know specifically if, say Ross or Pugh's book teaches this. I have read the first two chapters of Rudin's P.M.A. and found the exercises in the first chapter extremely difficult and decided I had some gaps in my knowledge to correct. As of this moment I would like to remedy this deficiency and then move on the Spivak's Calculus on Manifolds but I am interested in working through Rudin's P.M.A. prior. I am also currently working through Artin's Algebra book as well for whatever that is worth. Also I have one question about Spivak's Calculus on Manifolds book. I have not learned directional derivatives and understand that these are left as exercises in his book, which would make one think these are not that important whereas he focuses on total derivatives or what you may name them. Therefore I am asking if it is worthwhile to pursue the topic of directional derivatives from another source or just learn solely from Spivak's book? Thank you for your time [/QUOTE]
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Spivak Calculus on Manifolds and Epsilon delta proofs
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