Overall, the text is fairly clear, but I think it could be edited for precision in links and wording. Moreover, the text makes reference to Fermat's Theorem, when they in fact meant the 2nd derivative test. Such questions in the HW will leave the students wondering what exactly is being asked. For example, in the minimizing/maximizing section, the 'partial derivatives test' is referenced, but never defined. There are times when incorrect references are made and instructions are unclear. I find that students are weak in this area (parametric equations) and the review would be helpful. What I appreciated was the book beginning with 'parametric equations and polar coordinates.' Of course, this is suppose to be standard material in a Calculus II course, but perhaps this is evidence of "Calculus 3"-creep into "Calculus 2". That said, if what one considers 'calculus 3' changes as a result of students being less prepared, then this text will need to be updated to account for students with weaker foundations. The mathematics at this level is on a firm footing and will not be changing for the foreseeable future. Additionally, some figures are not entirely accurate and are misleading, e.g., the figure on continuity (the image of the open disk should not then again be an open disk on the surface, rather the image of such). The reason for the '4' in this category is that there could be many more figures, especially in the later sections on minimizing and maximizing functions and multivariable functions (viewing the level curves in conjunction with the surface). That said, I would have liked to see something on the higher-order derivative test. All of the important topics are covered and the examples are very thorough. Reviewed by Rob Niemeyer, Assistant Professor, Metropolitan State University of Denver on 10/21/19 Journalism, Media Studies & Communications +.
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