Calculus of Several Variables

✍ Scribed by Serge Lang (auth.)

• Publisher: Springer-Verlag New York
• Year: 1987
• Tongue: English
• Leaves: 623
• Series: Undergraduate Texts in Mathematics
• Edition: 3
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Front Matter....Pages 1-1
Vectors....Pages 3-48
Differentiation of Vectors....Pages 49-65
Functions of Several Variables....Pages 66-86
The Chain Rule and the Gradient....Pages 87-120
Front Matter....Pages 121-121
Maximum and Minimum....Pages 123-142
Higher Derivatives....Pages 143-179
Front Matter....Pages 181-181
Potential Functions....Pages 183-205
Curve Integrals....Pages 206-232
Double Integrals....Pages 233-268
Green’s Theorem....Pages 269-290
Front Matter....Pages 291-291
Triple Integrals....Pages 293-317
Surface Integrals....Pages 318-364
Front Matter....Pages 365-365
Matrices....Pages 367-384
Linear Mappings....Pages 385-411
Determinants....Pages 412-433
Applications to Functions of Several Variables....Pages 434-452
The Change of Variables Formula....Pages 453-486
Back Matter....Pages 487-I7

✦ Subjects

Real Functions