An Introduction to Multivariable Analysis

The subject of multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This introductory text provides graduate students and researchers in the above fields with various ways of handling some of the useful but difficult concepts encountered in dealing with the machinery of differential forms on manifolds. The approach here is to make such concepts as concrete as possible.
Highlights and key features:

• systematic exposition, supported by numerous examples and exercises from the computational to the theoretical
• brief development of linear algebra in RN, presenting concepts that figure prominently later in the book
• review of the elements of metric space theory
• treatment of standard multivariable material: differentials as linear transformations, the inverse and implicit function theorems, Taylor's theorem, the change of variables for multiple integrals (the most complex proof in the book)
• Lebesgue integration introduced in a concrete way rather than via measure theory. This involves certain series 'expansions' of functions, reduces the theory of integration to that of absolutely convergent series, which in the latter chapters serves to simplify the definition of integration of real-valued functions on manifolds
• latter chapters move beyond RN to manifolds and analysis on manifolds, covering the wedge product, differential forms, and the generalized Stokes' theorem
• bibliography and comprehensive index

Table of contents

Preface
Vectors and Volumes
Metric Spaces
Differentiation
The Lebesgue Integral
Integrals on Manifolds
K-Vectors and Wedge Products
Vector Analysis on Manifolds
Bibliography
Index