# Calculus of Several Variables

• Serge Lang
Textbook

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

1. Front Matter
Pages i-xii
2. ### Basic Material

1. Front Matter
Pages 1-1
2. Serge Lang
Pages 3-48
3. Serge Lang
Pages 49-65
4. Serge Lang
Pages 66-86
5. Serge Lang
Pages 87-120
3. ### Maxima, Minima, and Taylor’s Formula

1. Front Matter
Pages 121-121
2. Serge Lang
Pages 123-142
3. Serge Lang
Pages 143-179
4. ### Curve Integrals and Double Integrals

1. Front Matter
Pages 181-181
2. Serge Lang
Pages 183-205
3. Serge Lang
Pages 206-232
4. Serge Lang
Pages 233-268
5. Serge Lang
Pages 269-290
5. ### Triple and Surface Integrals

1. Front Matter
Pages 291-291
2. Serge Lang
Pages 293-317
3. Serge Lang
Pages 318-364
6. ### Mappings, Inverse Mappings, and Change of Variables Formula

1. Front Matter
Pages 365-365
2. Serge Lang
Pages 367-384
3. Serge Lang
Pages 385-411
4. Serge Lang
Pages 412-433
5. Serge Lang
Pages 434-452
6. Serge Lang
Pages 453-486
7. Back Matter
Pages 487-I7

### Introduction

The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.

### Keywords

Fourier series calculus derivative differential equation maximum minimum

#### Authors and affiliations

• Serge Lang
• 1
1. 1.Department of MathematicsYale UniversityNew HavenUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-1068-9
• Copyright Information Springer-Verlag New York Inc. 1987
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-7001-0
• Online ISBN 978-1-4612-1068-9
• Series Print ISSN 0172-6056
• Buy this book on publisher's site