Mathematical Analysis II (Universitext)

Zorich, V. A.

ISBN 10: 3662489910 / ISBN 13: 9783662489918

Editore: Springer, 2016

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Dati bibliografici

• Titolo: Mathematical Analysis II (Universitext)
• Editore: Springer
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 3662489910
• ISBN 13: 9783662489918
• Rilegatura: hardcover
• Edizione: seconda edizione
• Condizione: Good

Descrizione articolo

Riassunto

This secondEnglish edition of a very popular two-volume work presents a thorough firstcourse in analysis, leading from real numbers to such advanced topics asdifferential forms on manifolds; asymptotic methods; Fourier, Laplace, andLegendre transforms; elliptic functions; and distributions. Especially notablein this course are the clearly expressed orientation toward the naturalsciences and the informal exploration of the essence and the roots of the basicconcepts and theorems of calculus. Clarity of exposition is matched by a wealthof instructive exercises, problems, and fresh applications to areas seldomtouched on in textbooks on real analysis.

The maindifference between the second and first English editions is the addition of aseries of appendices to each volume. There are six of them in the first volumeand five in the second. The subjects of these appendices are diverse. They aremeant to be useful to both students (in mathematics and physics) and teachers,who may be motivated by different goals. Some of the appendices are surveys,both prospective and retrospective. The final survey establishes importantconceptual connections between analysis and other parts of mathematics.

This second volumepresents classical analysis in its current form as part of a unifiedmathematics. It shows how analysis interacts with other modern fields ofmathematics such as algebra, differential geometry, differential equations,complex analysis, and functional analysis. This book provides a firm foundationfor advanced work in any of these directions.

Informazioni sull?autore

VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences.