Ebook: Functions of Several Variables

The purpose of this book is to give a systematic development of differential
and integral calculus for functions of several variables. The traditional topics
from advanced calculus are included: maxima and minima, chain rule, implicit
function theorem, multiple integrals, divergence and Stokes’ theorems, and so
on. However, the treatment differs in several important respects from the traditional
one. Vector notation is used throughout, and the distinction is maintained
between n-dimensional euclidean space and its dual. By introducing
convex and concave functions a more thorough treatment of extrema is possible.
The elements of the Lebesgue theory of integrals are given. In place of the traditional
vector analysis, we first introduce exterior algebra and the calculus
of exterior differential forms.
The book is suitable for a college course at the advanced undergraduate level.
By omitting certain chapters, a one semester course can be based on it.