The second addition - after 50 years ! - is essentially the same as the original and remains full of the insights into the meaning and use of vectors that made this book such a hit among my friends studying physics and engineering some 40 years ago. Improvements are: the inclusion of solutions to 'supplementary problems' - essential to self study; an introduction - not always so successful - to some new topics, which are used in related studies; an illustrative example given directly after the introduction of some concepts. Annoyingly a few diagrams, at least one example and even a sentence have not been copied correctly from the original version, rendering these one or two diagrams in particular useless. Time wasted changing 'which' to 'that' and 'e.g.' and 'i.e.' to their full English equivalents could have been spent more usefully editing out these faults. In spite of this, the book is now a hit also with me as I have another go at understanding vectors.
This book can represent a good guide for undergrads students studying problems in the field of vector calculus. It's clearly written , summarizes needed derivations. There is a needed to increase the number of solved examples and make them more related to applied physics problems. For a researcher working in the field of electro magnetic's and fluid mechanics then this book can be your companion. The last chapter can provide you with essential basics for tensor calculus which in application can be related to mesh generation and differential geometry.
If you are a physics undergraduate student like me, you MUST have this book. Everything in it is needed. It is well explained, full of examples, very compact. You will learn fast, well and easy. No regrets really. Simply the best.
If you're intrested in learning vector calculus, this is the book to have. Each topic is well explained and I particularly like the plethora of problems with solved solutions that follow it. If you are still not satisfied, you can try your newly learned skills on the supplementary problems (answers supplied). The included introduction to tensors is a plus.
Very good explanation on the basics, especially on the proofs in the exercises. Section on tensors does not cover the concepts in depth, more on manipulations of tensors which is useful if you understand the the concepts already but just want to know the proofs.