# Multivariable Calculus with Applications

## Benefits

• 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

Textbook

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

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

### Introduction

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

#### Authors and affiliations

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

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 https://doi.org/10.1007/978-3-319-74073-7
• 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
• Buy this book on publisher's site
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