Active Calculus Multivariable

September 15, 2017 | Updated: May 8, 2020
Author: Steve Schlicker, David Austin, Matt Boelkins; Grand Valley State University

In Active Calculus Multivariable, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer plausibility arguments for such results, rarely do we include formal proofs. It is not the intent of this text for the instructor or author to demonstrate to students that the ideas of calculus are coherent and true, but rather for students to encounter these ideas in a supportive, leading manner that enables them to begin to understand for themselves why calculus is both coherent and true.

Subject Areas
Math/Stats, Calculus

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The Active Calculus-Multivariable cover image by James Haefner Photography is used under a CC BY-NC-SA license (

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Active Calculus Multivariable by Steve Schlicker, David Austin, Matt Boelkins; Grand Valley State University is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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Reviews (1) Avg: 4 / 5

Mehrzad Tabatabaian

Institution:BC Institute of TechnologyTitle/Position: FacultyCreative Commons License

Q: The text covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary

The coverage is comparable with TOC. However, the topic of 'Function of a Complex Variable' could be added as a chapter in the text a suggestion that fits the scope of this textbook.
The equations are not numbered in total, some are some are not.
cross-reference to Equation are not adequately cited.
on page 2, the definition of the variables for the equation is not complete.
Table 9.3, requires identifying of the Units for the variables used )i.e., x in ft, y in rad, and g=32.2 ft/s2)
use boldface letter for g, the gravitational acceleration, a vector.
on page 47, the equation mentioned is incorrect, should read T=rXF (not Fxr), throughout the chapter, as well.

Comprehensiveness Rating: 3 out of 5

Q: Content is accurate, error-free and unbiased

see comment in previous page.
there are some errors and some edits, as mentioned.

Content Accuracy Rating: 4 out of 5

Q: Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement

With addition of some examples related to technology and engineering practice, the text could become more relevant and useful for engineering students, as well.

Relevance Rating: 4 out of 5

Q: The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used

the text is written for students in the field of mathematics. If meant to be used for engineering students, as their math courses material, more relevant example are recommended.

Clarity Rating: 4 out of 5

Q: The text is internally consistent in terms of terminology and framework


Consistency Rating: 4 out of 5

Q: The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The text should not be overly self-referential, and should be easily reorganized and realigned with various subunits of a course without presenting much disruption to the reader.


Modularity Rating: 3 out of 5

Q: The topics in the text are presented in a logical, clear fashion

yes. However, adding the topic of Function of a complex variable, is recommended.

Organization Rating: 4 out of 5

Q: The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader

Table 9.3 and section/Activity 9.14 are suggested for edits/re-visit.
on page 28, first line, cross-reference Equation 9.2.

Interface Rating: 4 out of 5

Q: The text contains no grammatical errors

didn't find any.

Grammar Rating: 5 out of 5

Q: The text is not culturally insensitive or offensive in any way. It should make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds


Cultural Relevance Rating: 5 out of 5

Q: Are there any other comments you would like to make about this book, for example, its appropriateness in a Canadian context or specific updates you think need to be made?

The coverage of topics and its interactive feature is useful for students learning the material. As mentioned, adding some engineering related examples, function of a complex variable topic, numbering the equations would add to the value and usefulness of the book.