This book contains no offensive material. I didn’t find any conspicuous grammatical errors. It is well written with clear and straightforward English. The flow of the content is smooth and clear. Images and charts are properly formatted with little distortion. Further explanation of certain ideas can be found in a number of books referenced in the foot notes. The content is arranged basically the same way as in other standard books on this subject.Ī bibliography is compiled. It follows a logical sequence of the topics from vectors in Euclidean space to vector-valued functions, then functions of several variables, and finally line and surface integrals. Reorganization would be relatively hard due partly to the logical dependence of the topics, which is typical for math textbooks, and partly to the fact that this book is already lean. An instructor can easily organize the content into units to suit the flow in their class. Each chapter is then divided into a number of sections. The main content is divided into four chapters. Math styles and different fonts are used appropriately and consistently. The examples, definitions, theorems, and figures are numbered separately and sequentially in each chapter. The notations and terms used are consistent throughout the book. A good student should be able to understand most of the content through self-study. Very few long examples with tedious calculations are included. Good quality figures are generated and included to illustrate the ideas. Fully worked out examples are given as appropriate. Mathematical concepts are sufficiently explained. Expansion, if desired, can be done in future updates. There is such a need among senior or beginning graduate level STEM students.
VECTOR CALCULUS SERIES
I personally prefer that it contains some more advanced topics, such as the implicit function theorem and the Taylor series expansion of multivariable functions, and more involved real world examples in physical sciences so that it can also be used as a vector calculus textbook following the calculus sequence. Or one can use the book by selecting the topics one likes and supplements it with content found elsewhere. The book is for those who share a similar preference over the topics as the author. Many relevant topics are omitted, only briefly treated, or left as exercises. The proofs for some theorems are provided, while some others are left as exercises. It is well written with mathematical accuracy. This is a neatly organized little book on vector calculus. Answers and hints to selected exercises are provided in Appendix A toward the end of the book.
Color-coded boxes are used in the text to highlight the definitions, theorems, and other important results. A number of routine examples are provided to demonstrate mathematical concepts and basic techniques in calculation. At the end of each section a fair number of exercises are provided, which are divided into 3 categories, A, B, C, roughly based on the level of difficulty. It is relatively easy to read and follow. This book contains about enough material for a one semester multivariable calculus or a beginning vector calculus course. Reviewed by Yaping Liu, Professor, Pittsburg State University on 1/12/23
0 kommentar(er)
