EAN: 9788132221036

SMOOTH MANIFOLDS - RAJNIKANT SINHA GEBUNDEN

This book offers an introduction to the theory of smooth manifolds  helping students to
familiarize themselves with the tools they will need for mathematical research on smooth
manifolds and differential geometry. The book primarily focuses on topics concerning
differential manifolds  tangent spaces  multivariable differential calculus  topological
properties of smooth manifolds  embedded submanifolds  Sard's theorem and Whitney embedding
theorem. It is clearly structured  amply illustrated and includes solved examples for all
concepts discussed. Several difficult theorems have been broken into many lemmas and notes
(equivalent to sub-lemmas) to enhance the readability of the book. Further  once a concept has
been introduced  it reoccurs throughout the book to ensure comprehension. Rank theorem  a vital
aspect of smooth manifolds theory  occurs in many manifestations  including rank theorem for
Euclidean space and global rank theorem. Though primarily intended for graduate students of
mathematics  the book will also prove useful for researchers. The prerequisites for this text
have intentionally been kept to a minimum so that undergraduate students can also benefit from
it. It is a cherished conviction that mathematical proofs are the core of all mathematical joy
a standpoint this book vividly reflects.

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