OER Reviewed: CLP 1 Differential Calculus (UBC)

Reviewer: Shirin Boroushaki, Assistant Teaching Professor, Faculty of Mathematics and Statistics, Thompson Rivers University

OER was used for teaching by reviewer at UBC.

Rating
Each criterion asks the reviewer to rate it on a scale of 1 to 5 (1 = very poor and 5 = excellent).

Comprehensiveness – Rating: 4

The OER covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary.

Some minor topics are not fully covered in the text:

• Examples involve graph of the derivative: Given the notion of the derivative, other than Example 3.1.1, there are no examples involving graphing the derivative of a function given the function itself or vice versa. Also examples where critical values and local extrema are to be found given the graph of f’ are missing.
• Newton’s method of approximation is not covered in this OER.

Content Accuracy – Rating: 5

Content, including diagrams and other supplementary material, is accurate, error-free, and unbiased.

Relevance/Longevity – Rating: 5

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

Clarity – Rating: 4

The OER is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used.

There are a few concepts that may need more elaboration:

• Infinite limits and vertical asymptotes: The algebraic methods of evaluating limits are covered in Section 1.4 including infinite limits. There are only two examples of infinite limits (Examples 1.4.6 and 1.4.7) where the explanation is limited to “non-zero/zero=DNE”, whereas these limits usually need a more in-depth analysis and some graphical interpretation in the form of vertical asymptotes. On a similar note, in Section 2.2, the concept of non-differentiability for functions with a vertical tangent line is delivered as DNE limits with no mention of infinity as the value of the derivative limit.
• Horizontal asymptote as the geometric interpretation of limits at infinity: Similarly, in Section 1.5 where “Limits at infinity” are introduced, there is no mention of horizontal asymptote as a graphical interpretation of such limits. The notion of “Asymptotes” is briefly covered in two paragraphs in Section 3.6 followed by one example where they are needed for curve sketching.

Consistency – Rating: 5

The OER is internally consistent in terms of terminology and framework.

Modularity – Rating: 5

The OER 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 OER 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.

Organization/Structure/Flow – Rating: 4

The topics in the OER are presented in a logical, clear fashion.

The following reordering may be taken into account:

• Rolle’s Theorem is normally covered after the discussion of increasing and decreasing functions and extrema because its proof depends on those concepts, whereas in this OER, MVT and Rolle’s Theorem are introduced earlier in Chapter 2. Given that the proof of Rolle’s Theorem is not included in the text, the different order has not affected the logical flow of topics, but re-ordering of the topics in Sections 2.13, 3.5.1 and 3.6.2 may be considered if one wishes to include proofs.
• The concept of approximations with Taylor polynomials is included in full details in this text. One may consider moving the Taylor series and some of the expanded arguments therein to CLP2 where series and sigma notation are fully introduced.

Interface – Rating: 5

The OER 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.

Grammatical/Spelling Errors – Rating: 5

The OER contains no grammatical or spelling errors.

Diversity and Inclusion – Rating: N/A

The OER reflects diversity and inclusion regarding culture, gender, ethnicity, national origin, age, disability, sexual orientation, education, religion. It does not include insensitive or offensive language in these areas.

The majority of concepts in calculus involves directly numbers and formulas. There are some word problems modelling real-life applications of certain concepts but these applications are mainly in natural sciences and they rarely involve an aspect of diversity and inclusion.

Recommendation

1. 1. Do you recommend this resource for the specific course taught in the first-year engineering common curriculum (in place of a commercially available resource)?
      Yes, this textbook is recommended.
   2. If yes, please briefly summarize the reasons for recommending this resourceIt covers almost all the topics that are normally taught in a first-year differential calculus course in engineering and they are organized in a clear and logical order. Each section includes several examples, more exercises and practice problems are covered in a separate problem book that also includes answers to problems. There is also a version of the textbook where the text and problems are combined in one single pdf.
   3. What gaps in content have you identified?
      Summary of some possible adjustments:

• • More elaboration on infinite limits and the geometric interpretation of limits involving infinity as asymptotes in general.
  • More examples involving the graphical interpretation of the derivative and relating a function and its derivative by using graphical properties.
  • Missing topic: Newton’s method.