Overview
- Offers important geometric approach to advanced calculus
- Integrates text fully with 250+ illustrations
- Treats classical advanced calculus topics Uses 2D and 3D graphics to study maps
- Magnifies images to carry out local analysis
- Gives visual insight into the derivative
- Gives geometric interpretation of implicit function theorems
- Analyzes physical meaning of divergence and curl Presents Morse's lemma and Poincaré lemma
- Includes supplementary material: sn.pub/extras
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (11 chapters)
Keywords
About this book
Reviews
From the reviews:
“Many concepts in calculus and linear algebra have obvious geometric interpretations. … This book differs from other advanced calculus works … it can serve as a useful reference for professors. … it is the adopted course resource, its inclusion in a college library’s collection should be determined by the size and interests of the mathematics faculty. Summing Up … . Upper-division undergraduate through professional collections.” (C. Bauer, Choice, Vol. 48 (8), April, 2011)
“The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. … The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. … Strong students … are likely to be attracted by the approach and the serious meaty content.” (William J. Satzer, The Mathematical Association of America, January, 2011)
“A new geometric and visual approach to advanced calculus is presented. … The book can be useful a textbook for beginners as well as a source of supplementary material for university teachers in calculus and analysis. … the book meets a wide auditorium among undergraduate and graduate students in mathematics, physics, economics and in other fields which essentially use mathematical models. It is also very interesting for teachers and instructors in Calculus and Mathematical Analysis.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1205, 2011)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Advanced Calculus
Book Subtitle: A Geometric View
Authors: James J. Callahan
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4419-7332-0
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+BusinessMedia, LLC 2010
Hardcover ISBN: 978-1-4419-7331-3Published: 17 September 2010
Softcover ISBN: 978-1-4939-4070-7Published: 23 August 2016
eBook ISBN: 978-1-4419-7332-0Published: 09 September 2010
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: XVI, 526
Topics: Real Functions, Analysis, Applications of Mathematics, Approximations and Expansions