OER Reviewed: CLP 2 Integral 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.

A few topics need more emphasis:

In Chapter 1:

• The idea of approximating area under a curve by rectangles is introduced as one motivational example in Section 1.1 and a few pages later the sigma definition of the definite integral is given. The same motivational example is used again for Riemann sum evaluation. This is the only example done in the text for area approximation using Riemann sums with finite number of rectangles. To introduce the idea of the integral one may need to include more examples of Riemann sums before moving on to the limit definition of the integral where the number of rectangles tends to infinity.
• Given the limit/sigma definition of the integra, there are no examples to evaluate an integral using the definition and vice versa, i.e., examples where a given limit of a summation can be written as a definite integral. Some of these missing examples from the text are included in the problem book only.
• The section on “Volumes” only covers examples where the region is revolved around x or y axis. Examples where the axis of revolution is x=a or y=a are not included in the text; the problem book, however, contains some questions of this sort.

In Chapter 2:

• The application of the integrals as the “net change in some quantity” can be expanded more in this chapter. This application is briefly touched in Example 1.1.18 and later in Chapter 2 it is only discussed in the context of “work”. More applied examples in engineering can be included.
• The topic of “Arc length” is not included in the application of integration.

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.

In Section 2.4 where the application of integration in differential equations is discussed, the method of solving separable equations is delivered without providing sufficient introductory knowledge to differential equations. Although engineering students may pass a full course on differential equations in their 2nd or 3rd year, this is the first time they encounter the concept of differential equations, so it would seem more reasonable to introduce what a differential equation and its solution are before discussing one particular family of such equations.

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.

Possible re-ordering:

• Riemann sums are introduced after the definition of the definite integral, however, they are typically introduced earlier so that they can be used to lay out the idea of definite integral as an area.
• The section on “Volumes” can be moved to Chapter 2 as it is usually considered as an application of integration.

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 resource
      This OER is recommended. Except one or two minor topics, it covers all the topics that are taught in a first-year integral calculus course in engineering.
   3. What gaps in content have you identified?
      Below is the summary of some gaps observed in the OER:

1. • Adequate elaboration and examples on approximating areas using Riemann sums.
   • Examples aimed for understanding the sigma definition of the definite integral, i.e., converting integrals into limit of summations and vice versa.
   • Examples of volume calculation for revolution of a region around axes other than x and y.
   • More elaboration on applications of integrals as the total change.
   • Adequate context for Differential Equations before introducing a method of solving them.
   • Missing topic: Arc length calculation.What gaps in content have you identified?
     
     It is noted that some of the missing examples are included in the problem book, hence, one may consider embedding a number of those questions into the text.