Calculus of Several Variables

✍ Scribed by Serge Lang

• Publisher: Springer
• Year: 1987
• Tongue: English
• Leaves: 633
• Series: Undergraduate Texts in Mathematics
• Edition: 3
• Category: Library

✦ Synopsis

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

✦ Table of Contents

Front Cover
Title Page
© Page
Foreword
Contents
Part One Basic Material
CHAPTER I Vectors
CHAPTER II Differentiation of Vectors
CHAPTER III Functions of Several Variables
CHAPTER IV The Chain Rule and the Gradient
Part Two Maxima, Minima, and Taylor's Formula
CHAPTER V Maximum and Minimum
CHAPTER VI Higher Derivatives
Part Three Curve Integrals and Double Integrals
CHAPTER VII Potential Functions
CHAPTER VIII Curve Integrals
CHAPTER IX Double Integrals
CHAPTER X Green's Theorem
Part Four Triple and Surface Integrals
CHAPTER XI Triple Integrals
CHAPTER XII Surface Integrals
Part Five Mappings, Inverse Mappings, and Change of Variables Formula
CHAPTER XIII Matrices
CHAPTER XIV Linear Mappings
CHAPTER XV Determinants
CHAPTER XVI Applications to Functions of Several Variables
APPENDIX Fourier Series
Answers to Exercises
Index
Back Cover