Calculus of Several Variables

This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included.

Inhalt
One Basic Material.- I Vectors.- II Differentiation of Vectors.- III Functions of Several Variables.- IV The Chain Rule and the Gradient.- Two Maxima, Minima, and Taylor's Formula.- V Maximum and Minimum.- VI Higher Derivatives.- Three Curve Integrals and Double Integrals.- VII Potential Functions.- VIII Curve Integrals.- IX Double Integrals.- X Green's Theorem.- Four Triple and Surface Integrals.- XI Triple Integrals.- XII Surface Integrals.- Five Mappings, Inverse Mappings, and Change of Variables Formula..- XIII Matrices.- XIV Linear Mappings.- XV Determinants.- XVI Applications to Functions of Several Variables.- XVII The Change of Variables Formula.- Appendix Fourier Series.- §1. General Scalar Products.- §2. Computation of Fourier Series.- Answers to Exercises.