Authors:
- Describes theoretical as well as practical aspects of multivariable calculus
- Correlates concepts and results of multivariable calculus with their counterparts in one-variable calculus
- Presents a wealth of problems varying degrees of difficulty
- Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems.
Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics.Keywords
- Multivariable Calculus textbook
- Vectors and matrices
- Functions of several variables
- tangent plane
- partial derivatives
- Inverse functions
- Differentiable functions
- differentiation in physics
- Double integrals
- area, volume and integral
- Green’s formula
- Divergence Theorem
- Vector Calculus
- Calculus III
- Partial differential equations
- Vector Analysis
Reviews
“This book belongs to a collection aimed at third- and fourth-year undergraduate mathematics students at North American universities. … There are more than 200 figures to help the reader to understand the explanations and about 500 problems. … I think this book can be recommended since, moreover, it is very pedagogical.” (Richard Becker, Mathematical Reviews, October, 2018)
“Lax and Terrell’s sequel to their Calculus With Applications presents a first course in multivariable calculus that fits in just over 400 pages. Even instructors who use standard texts will find much of value in this refreshing first edition. The book is written with a wide range of STEM students in mind, and its exposition remains remarkably fluid without scarificing precision. Every section of each chapter ends with an excellent collection of exercises, which should be graciously welcomed by independent learners and instructors alike.” (Tushar Das, MAA Reviews, September, 2018)
“The main achievement of the authors is that they essentially have simplified the teaching of the old topics to make a place for new ones. The proofs are exposited to encourage understanding, not meaningless rigor. … the presented book is a useful tool for all mathematicians (not only for students) and I find it regrettable that this book was not written when I was a student.” (Andrey Zahariev, zbMATH 1396.26002, 2018)
Authors and Affiliations
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Courant Institute of Mathematical Sciences, New York University, New York, USA
Peter D. Lax
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Department of Mathematics, Cornell University, Ithaca, USA
Maria Shea Terrell
About the authors
Maria Shea Terrell is currently a retired Senior Lecturer in Mathematics at Cornell University.
Bibliographic Information
Book Title: Multivariable Calculus with Applications
Authors: Peter D. Lax, Maria Shea Terrell
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-74073-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2017
Hardcover ISBN: 978-3-319-74072-0Published: 27 March 2018
Softcover ISBN: 978-3-030-08913-9Published: 11 December 2018
eBook ISBN: 978-3-319-74073-7Published: 12 March 2018
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: VIII, 483
Number of Illustrations: 230 b/w illustrations, 1 illustrations in colour
Topics: Analysis, Applications of Mathematics