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Fundamental Concepts In Modern Analysis: An Introduction To Nonlinear Analysis (Hardcover, Second Edition)
Loot Price: R2,695
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Fundamental Concepts In Modern Analysis: An Introduction To Nonlinear Analysis (Hardcover, Second Edition)
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Many applied mathematical disciplines, such as dynamical systems
and optimization theory as well as classical mathematical
disciplines like differential geometry and the theory of Lie
groups, have a common foundation in general topology and
multivariate calculus in normed vector spaces. In this book,
students from both pure and applied subjects are offered an
opportunity to work seriously with fundamental notions from
mathematical analysis that are important not only from a
mathematical point of view but also occur frequently in the
theoretical parts of, for example, the engineering sciences. The
book provides complete proofs of the basic results from topology
and differentiability of mappings in normed vector spaces. It is a
useful resource for students and researchers in mathematics and the
many sciences that depend on fundamental techniques from
mathematical analysis.In this second edition, the notions of
compactness and sequentially compactness are developed with
independent proofs for the main results. Thereby the material on
compactness is apt for direct applications also in functional
analysis, where the notion of sequentially compactness prevails.
This edition also covers a new section on partial derivatives, and
new material has been incorporated to make a more complete account
of higher order derivatives in Banach spaces, including full proofs
for symmetry of higher order derivatives and Taylor's formula. The
exercise material has been reorganized from a collection of problem
sets at the end of the book to a section at the end of each chapter
with further results. Readers will find numerous new exercises at
different levels of difficulty for practice.
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