© 2017

Multivariable Calculus with Applications


  • 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


Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Peter D. Lax, Maria Shea Terrell
    Pages 1-62
  3. Peter D. Lax, Maria Shea Terrell
    Pages 63-102
  4. Peter D. Lax, Maria Shea Terrell
    Pages 103-159
  5. Peter D. Lax, Maria Shea Terrell
    Pages 161-190
  6. Peter D. Lax, Maria Shea Terrell
    Pages 191-204
  7. Peter D. Lax, Maria Shea Terrell
    Pages 205-278
  8. Peter D. Lax, Maria Shea Terrell
    Pages 279-332
  9. Peter D. Lax, Maria Shea Terrell
    Pages 333-385
  10. Peter D. Lax, Maria Shea Terrell
    Pages 387-419
  11. Back Matter
    Pages 421-483

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.


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

Authors and affiliations

  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of MathematicsCornell UniversityIthacaUSA

About the authors

Peter D. Lax is currently an Emeritus Professor of Mathematics at the Courant Institute of Mathematical Sciences.

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
  • Series Abbreviated Title Undergraduate Texts Mathematics
  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-74072-0
  • Softcover ISBN 978-3-030-08913-9
  • eBook ISBN 978-3-319-74073-7
  • 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
  • Buy this book on publisher's site
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“The presentation of the material is guided by applications so that physics and engineering students will find the text engaging and see the relevance of multivariable calculus to their work. The text contains over 500 exercises with answers and/or solutions to half provided at the back of the book, enabling students to gauge their understanding of the content as they proceed. A well-written, engaging text. Summing Up: Highly recommended. Upper-division undergraduates and professionals.” (J. T. Zerger, Choice, Vol. 56 (03), November, 2018)

“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)