Vector Calculus by Paul C. Matthews (PDF)

Description

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

User’s Reviews

Editorial Reviews: Review P.C. MatthewsVector Calculus”Written for undergraduate students in mathematics, the book covers the material in a comprehensive but concise manner, combining mathematical rigor with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which essential for a full understanding of the subject.” ― ZENTRALBLATT MATH

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There are many books on Vector Calculus including the original Vector Analysis by Wilson based on the Gibbs Yale lectures published in 1901 (now in the public domain and available free on line). However, some modern conventions such as suffix notation, use of the Kronecker delta and Levi-Civita symbols, have been introduced since then and can be a source of some confusion. This book gives a very clear and concise explanation of both the basics and these newer conventions. Highly recommended for the self-learner.

⭐its selection of problems and its focus on vector calculus are both quite good. Perhaps both are excellent, but my current experience and intuition in this subject area prevent me from being more certain.Either way, a much more physically intuitive approach with more problem-solution examples and less geometrical rigor is possible, that much is certain.Most importantly, in-text solutions are provided. There is no problem with merely an answer, all have something more. There are way fewer problems as compared to a schaum’s outline (on the order of 30 times fewer). Though it also costs two or three times more than a Schaum’s, it’s certainly much more physically intuitive than the Schaum’s on vector/tensor analysis by Murray R. Spiegel.I think this book would make its publisher and author a lot more money (by selling a hell of a lot more of them) if it were reduced in price. It would be a win-win for everybody who, I’m pretty certain, matters here.

⭐It is great to read for students who major the subject, but to those who are not, it does not fit.

⭐This is a good introductory overview for people new to the subject, or who need to dip into it for an application. It quickly gets to the point and tells you what everything means. But it has one quirk: The author thinks the plural of “suffix” is “suffices.” It is not and never has been. It is “suffixes.” In Latin the x was not the last letter of the word.

⭐It is good for engineers.

⭐I bought this book based on the other good reviews here and I was solely dissapointed. I have a Degree in Physics and Engineering and a Masters in Engineering as well and I bought this book to brush up my rusty fundamentals in prepping for a new job that involves a heavy amount of Electromagnetics which naturally means going back and redoing my Vector Calculus. Mr.Mathew does not believe in delving deep into any subject. Note that this is a very thin book, the theme here is more a stating of the facts than a rigorous treatment that would delve into each building block of Vector Calculus. So, if you are looking for an in-depth approach, lots of solved problems then dont buy this book.

⭐It’s very direct, so while it doesn’t lead you astray, it also doesn’t hold your hand

⭐concise and clear. exercises are good too.

⭐The major problem is a lack of worked examples of the most elementary problems. Show me how to do the simple things and then I may have some hope of understanding the more advanced concepts. Understanding is only achieved by getting simple building blocks right and then adding the superstructure.

⭐A good book on Vector Calculus. All the key topics were clearly explained and demonstrated with plenty of exercises. It also explains the use of tensors as well as a way of calculating volume components which is much easier than finding the determinant of the Jacobian

⭐I bought this book because I wanted to revive my memories of div, grad, curl etc had faded over many years. The book is small and well focused. There’s no flab in it. I highly recommend it.

⭐I have just started to use this book, and it will take me a long time to complete this course.However, I like chapter one!

⭐Just bought this book because i was having trouble with vector and matracies analysis in bEng mechanical engineering. I am glad i made the right choice.

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