In some cases, some examples and exercises appear to belong more appropriately in another section.

It is first introduced with the second derivative test for extrema (Section 5.3) and concavity (Section 5.4). Schreiben Sie den ersten Kommentar zu "De Gruyter Textbook: Multi-Variable Calculus". The style of the book is to work from the concrete to the abstract, from the particular to the general. 4.3.''

  • Volumes by slicing, circular laminae, cylindrical shells. There present variety of reasons behind it due to which the readers stop reading the eBooks at their first most effort to use them.

    The internal hyperlinks in the pdf version of the text are a very nice feature, taking you instantly to a referenced diagram, definition, or solution of an exercise. Buch

    Organization of the material that is perhaps slightly unusual includes introducing the derivative before introducing continuity, leaving limits at infinity until later (Section 4.10), introducing integration by parts and integration of rational functions using partial fractions before any applications of integration.

    Single variable calculus, early transcendentals, in PDF format. These are very minor issues and they do not affect the effectiveness of the textbook.

  • Derivatives of trigonometric functions and their inverses.
  • the ratio and root tests. 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.

    Course Objectives: Students in MA2160 should be able to: Work a problem numerically, algebraically, graphically, and verbally (Rule of 4).

    It would have been helpful to have some visual representation of these rules, perhaps something like the following figure:

    image not available

    Visualizations for the Product and Chain Rules.

    For the most part the authors do not state general results, but rather expect the student either to imitate the process in the examples or to invent their own formulae. Further, Exercises 1, 2, and 22 are not in the right section since it does not require the Chain Rule to solve these problems. There is a link in Figure 2.1 to a \href{http://www.whitman.edu/mathematics/calculus/live/jsxgraph/secant_lines.html}{Sage worksheet} of the function $y=2x(1-x)$ in which one end of a secant line is fixed at $x=0.15$ but the other can be moved, so it is possible to watch the secant line approach the tangent line.

    Overall, I like this book a lot.

    For the second semester course some instructors might find this text missing some topics, such as first order differential equations.

    For a mathematician, the topics are presented in a clear, logical fashion.



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