Teaching English as a Foreign Language (TEFL).Computer-Aided Design (CAD) & Building Information Modeling (BIM).Prior experience with linear algebra is helpful, but not required. Otherwise the level of rigor is fairly normal. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. The presentation is geared towards students who enjoy learning mathematics for its own sake. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. This book covers the standard material for a one-semester course in multivariable calculus. 4 Real-valued functions: differentiation.II Vector-valued functions of one variable.Overall, I think this is an excellent text for multivariable calculus. Humor is scattered throughout, for example, including a picture of a porcupine as an example of a mammal with an orientation. The conversational style was great: "trying to find the maximum of a function like. (This tiptoes up to topology of the underlying space which the author has already alluded to at various places.) I think one addition to chapter 11 as a further teaser and to try to show the relationship of the various theorems, would be to set up the deRham sequence in R^3 and show how gradient, curl, and divergence come into that single unifying sequence. I liked the presentation of differential forms towards the end. It is more theoretical, more proof-based than what I usually teach, and I might skip some of that if I were teaching from this text, but I think it is good to include the proofs in the text. Good color illustrations showing geometric pictures when helpful. It easy to navigate jumping around with the bookmarks pane in Adobe. It might be helpful to introduce polar coordinates earlier. The preface and table of contents outline the organization and make it easy to find topics. The division into parts, chapters, and sections made sense and the sections were not too long. Good diagrams throughout, present whenever needed to help with understanding, e.g., showing the relationship of two different parametrizations when proving that the value of the integral is independent of the parametrization. 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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