Conditions of Use
As mentioned in the preface, the text is “designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence.” There are three chapters – Numbers & Functions, Basic Skills for Calculus, and Solving &... read more
As mentioned in the preface, the text is “designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence.” There are three chapters – Numbers & Functions, Basic Skills for Calculus, and Solving & Trigonometric Functions. The authors do a good job of covering all the common precalculus areas with which students struggle in calculus. (Factoring doesn’t include the cases where the leading coefficient is not equal to 1.) There is no index or glossary, however, solutions to the exercises are included.
The content is unbiased, however it is not error-free. While reading the text, I noticed more typographical, grammatical, and mathematical errors than I expected. (I plan on sending a copy of the errors that I found to the authors.)
The text is current and relevant for its intended audience. The authors do a good job connecting the topics to the real world to explain to the students why each topic is important.
The text is well-written and at a level that makes it very readable for students. It is clearly written with students as the intended audience. The explanations and solutions of examples are very clear and easy to follow.
The text is very consistent with content and worked examples and exercises. The consistency of the exercise sets especially stood out with questions about “Terms & Concepts” followed by problems of varying difficulty
There are a few places where the text refers to something done previously, but for the most part, an instructor could assign individual sections as needed.
For the most part the text is very well-organized and the topics are presented in a logical clear fashion. I did find the title of Chapter 3 (Solving and Trigonometric Functions) confusing. Since “Solving” and “Trigonometric Functions” are separate topics, I would suggest they be split into separate chapters.
The text is a pdf. There are no navigation problems. The graphics are clear and very helpful for the reader.
There are some grammatical errors. For example, in the first section there are several times when the singular “parenthesis” is used, when it should be the plural form “parentheses”. The word “term” is used at times, when it should be “factor” or “expression”. Of more concern are the mathematical errors scattered throughout the text.
I did not notice any places of concern for being culturally insensitive or offensive.
With a bit more editing, this will be a great text for students needing support with the common precalculus areas in which calculus students struggle. There are excellent examples throughout the text to illustrate the concepts. It is obviously intentionally written for students, with clear explanations, the inclusion of alternate wording students might run across, and motivation for learning the techniques and concepts. A wonderful resource!
Table of Contents
1 Numbers and Functions
- 1.1 Real Numbers
- 1.2 Introduction to Functions
- 1.3 Factoring and Expanding
- 1.4 Radicals and Exponents
- 1.5 Logarithms and Exponential Functions
2 Basic Skills for Calculus
- 2.1 Linear Functions
- 2.2 Solving Inequalities
- 2.3 Function Domains
- 2.4 Graphs and Graphing
- 2.5 Completing the Square
3 Solving and Trigonometric Functions
- 3.1 Solving for Variables
- 3.2 Intersections
- 3.3 Fractions and Partial Fractions Decomposition
- 3.4 Introduction to Trigonometric Functions
- 3.5 Trigonometric Functions and Triangles
About the Book
This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.
About the Contributors
Amy Givler Chapman, Ph.D., Department of Applied Mathematics, Virginia Military Institute
Meagan Herald, Ph.D., Department of Applied Mathematics, Virginia Military Institute
Jessica Libertini, Ph.D., Department of Applied Mathematics, Virginia Military Institute