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 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 multivariable analysis and 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
* 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 concrete way rather than
via measure theory
* latar 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
Core topics in multivariable analysis that are basic for senior
undergraduates and graduate studies in differential geometry and
for analysis in N dimensions and on manifolds are covered. Aside
from mathematical maturity, prerequisites are a one-semester
undergraduate course in advanced calculus or analysis, and linear
algebra. Additionally, researchers working in the areas of
dynamical systems, control theory and optimization, general
relativity and electromagnetic phenomena may use the book as a
self-study resource.
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