Overview
- Presents a precise and rigorous exposition of Stokes' theorem
- Takes a differential geometric point of view on vector calculus and analysis
- Designed as a textbook for upper-undergraduate students, and can also be useful for engineering and physics students?
- Includes supplementary material: sn.pub/extras
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Universitext (UTX)
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Table of contents (10 chapters)
Keywords
About this book
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Several practical methods and many solved exercises are provided. This book tries to show that vector analysis and vector calculus are not always at odds with one another.
Key topics include:
-vectors and vector fields;
-line integrals;
-regular k-surfaces;
-flux of a vector field;
-orientation of a surface;
-differential forms;
-Stokes' theorem;
-divergence theorem.
This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables. The book can also be useful to engineering and physicsstudents who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Vector Analysis Versus Vector Calculus
Authors: Antonio Galbis, Manuel Maestre
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4614-2200-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Softcover ISBN: 978-1-4614-2199-3Published: 26 March 2012
eBook ISBN: 978-1-4614-2200-6Published: 29 March 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIII, 375
Number of Illustrations: 20 b/w illustrations, 59 illustrations in colour
Topics: Global Analysis and Analysis on Manifolds, Differential Geometry, Mathematical Applications in the Physical Sciences