Nice treatment of multidimensional chain rule via matrix multiplication with one section on the conceptual picture and one on computations. This is not much of an issue for math texts.Įxcellent! Good clear explanations of the ideas behind the theory, e.g., Lagrange multipliers which are sometimes presented as magic, but here are motivated with geometrical ideas. The mathematics is all correct and the author is honest about where things are being swept under the rug, e.g., in the proof of Green's Theorem. Wobbling means going back and forth which can happen in the plane. He describes torsion as "wobbling" which to me gives the wrong idea. My only complaint here is in the discussion of torsion. I still give this text a 5 for comprehensiveness. In discussing multivariable continuity, it would have been nice to pull out the two path discussion which appears in the text and highlight it as a theorem, but these are all minor points. Some of my favorite examples were missing: e.g., the cycloid and deriving Kepler's laws from Newton's laws, but everybody has their own favorites so I am okay with that. The development was clear enough that I hope most students at this level could get it. I liked the development of differential forms towards the end and having chapter 11 as a teaser for higher level stuff. Reviewed by Andy Rich, Professor of Mathematics, PALNI, Manchester University on 12/19/19 Journalism, Media Studies & Communications +.
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