Vector Calculus (Dover Books on Mathematics)

This book is probably daunting for a beginner, but if you already are comfortable with linear algebra and some analysis, this is an excellent treatment of multivariable calculus. I feel that this book fills an important gap in my studies, in that after learning basic multivariable calculus I went on to analysis and topology of arbitrary spaces, but never really applied those topics to R^n. In that respect, this book was exactly what I was looking for.

Initially, I must admit that I was easily impressed by the compendious nature of the work in question. I realized early on that anyone tackling this particular work would surely have to bring a considerable amount of abstract mathematical sophistication to the table. I guess this was my greatest shortcoming (read, "blunder;error;miscalculation", etc.), truly a shortcoming that would in the end prevent me from deriving the most benefit possible from this work. Not wishing to take anything away from Messrs. Baxandall and Liebeck or to question their intellectual accomplishments, I just cannot get comfortable with the manner by which they purport to impart their vast knowledge to those wishing to use their work. While I have never believed that serious students should ever be mollycoddled, I also am not liable to easily cotton to being overwhelmed by immense knowledge that somehow cannot be readily and effectively transmitted to the ones being taught. Permit me to cite a relatively simple counterexample. In merely thumbing through a work by the late Richard Silverman, I came away satisfied that HE COULD teach me the proper techniques for determining surface areas. With Baxandall and Liebeck, I never felt that I was even going in that direction at all, when I read through what they had to say about surface integrals. I should be only too willing to put my discomfort down to my own lack of mathematical sophistication and readily admit that I could never be thought of being in the same class with Messrs. Baxandall and Liebeck. But, then again, their book was advertised as one capable of linking together various mathematical disciplines to enable the student to better make his/her way through vector calculus, as presented by the two authors above mentioned. Maybe others would be able to do so. I find it surely regrettable that I cannot. Sad to say, but, demonstrable intelligence and consummate command of one's subject are surely no guarantee of anyone's acumen in the critical matter of instructing others.

WAY TOO THEORETICAL FOR ME TO READ LOL :(((((((I GUESS ITS A GOOD READ IF YOU HAVE TIME TO REALLY TAKE IN THE CONCEPTS AND UNDERSTAND WHAT THIS COMPLICATED BOOK IS SAYING... IF YOU UNDERSTOOD THIS BOOK THEN YOU WOULD DEFINITELY GO BACK TO CLASS AND HAVE A CLEARER PICTURE... ITS SO DEEP THO, NOTHING PRACTICAL WITH AUTHORS EXPLANATIONS, ETC

I thank the authors for guiding me through this amazing journey through vector calculus, it is so simply and clearly written that even I could understand it.

Very nice book of vector calculus including "Elementary Differential Geometry". Explanation of the topics is fabulous.

Este libro está dirigido para todos aquellos que deseen aprender Cálculo Multivariable a través de la lectura, trae muy pocos ejercicios pero todos los temas vienen bastante bien explicados

Lo ví en una biblioteca de matemáticas, y me llamó la atención su estructura y la infinitud de ejemplos para ilustrar la teoría. Es un buen texto para complementar con otros más especializados, especialmente de geometría diferencial. Quizá haya que reforzarlo también en temas de topología diferencial, en lo que respecta a los teoremas de integración en campos vectoriales.