Vector Calculus Review

The field of vector calculus is a crucial aspect of multivariable calculus, yet it often presents significant challenges to students due to its complex nature. The chain rule, Jacobian, and other fundamental concepts must remain accessible without delving into linear algebra or making them seem ad hoc. This is particularly true for students who have not had prior exposure to these topics.

As a result, many calculus textbooks introduce vector analysis in a way that makes the subject work, but does not require prior knowledge of linear algebra. In fact, it is common for students to take a basic multivariable calculus course after completing two semesters of single-variable calculus.

The book under review addresses this issue by providing an introduction to vector calculus that is self-contained and concise. While it may not be possible to cover every aspect of the topic in-depth, the author has done an excellent job of making the subject accessible to students who are new to it.

Fortunately, readers can access a comprehensive review of the book online through JSTOR or with their MAA membership. Warwick Tucker's 2003 review provides an exhaustive summary of the second edition of this book and serves as an accurate evaluation of the current publication.

In fact, I believe that Warwick Tucker has done an outstanding job of reviewing the book, and readers would be well-served by consulting his article for a detailed understanding of the text. Therefore, I will not attempt to provide a comprehensive review here but instead refer readers to Tucker's excellent work.

In conclusion, this vector calculus review provides an introduction to the subject that is accessible and concise, making it an excellent resource for students who are new to multivariable calculus. With its self-contained approach and clear explanations, this book is an ideal choice for anyone looking to gain a solid understanding of vector calculus.

Vector calculus review