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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Functions Of Several Real Variables (Hardcover)
Loot Price: R3,831
Discovery Miles 38 310
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Functions Of Several Real Variables (Hardcover)
Expected to ship within 12 - 17 working days
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Total price: R3,851
Discovery Miles: 38 510
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This book begins with the basics of the geometry and topology of
Euclidean space and continues with the main topics in the theory of
functions of several real variables including limits, continuity,
differentiation and integration. All topics and in particular,
differentiation and integration, are treated in depth and with
mathematical rigor. The classical theorems of differentiation and
integration such as the Inverse and Implicit Function theorems,
Lagrange's multiplier rule, Fubini's theorem, the change of
variables formula, Green's, Stokes' and Gauss' theorems are proved
in detail and many of them with novel proofs. The authors develop
the theory in a logical sequence building one result upon the
other, enriching the development with numerous explanatory remarks
and historical footnotes. A number of well chosen illustrative
examples and counter-examples clarify matters and teach the reader
how to apply these results and solve problems in mathematics, the
other sciences and economics. Each of the chapters concludes with
groups of exercises and problems, many of them with detailed
solutions while others with hints or final answers. More advanced
topics, such as Morse's lemma, Sard's theorem, the Weierstrass
approximation theorem, the Fourier transform, Vector fields on
spheres, Brouwer's fixed point theorem, Whitney's embedding
theorem, Picard's theorem, and Hermite polynomials are discussed in
stared sections.
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