![]() 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. 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 Journalism, Media Studies & Communications +.Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Following the introduction of each new topic, worked examples are provided. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. This book assumes no previous knowledge of vectors. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. ![]() Vector calculus is the fundamental language of mathematical physics.
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