Mathematical Analysis II (Universitext) 2nd Edition by V. A. Zorich (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Gran libro. Un enfoque totalmente actual y un gran nivel. Desarrolla poderosas herramientas matemáticas para resolver problemas teóricos e increíbles aplicaciones físicas. En resumen un gran libro!I bought the English version of I, simplified Chinese version of II (directly translated from Russian)。They are not easy, but contains everything from single variable to vector analysis, and explained in detail.I like the part of differential forms the most, totally clear. This book also derive coordinate change formulas for div(and all that) from differential forms, which is rare among analysis books.

⭐Compré el volumen 1 hace unos años y la impresión es notablemente mejor. He usado el vol.1 mucho y casi no tiene desgaste en el lomo, hoy abrí el volumen 2 y ya hasta parece que se va a partir el lomo. La impresión parece casi de fotocopia. Ya he comprado dos o tres libros por amazon que parecen versiones piratas de los originales. No recomiendo comprar éste, y mucho menos por el precio al que lo venden. Si quieres el libro búscalo por otro lado.I bought the first volume in the series a couple of years ago and the quality is noticeably worse on vol.2. I’ve used volume 1 extensively and it show little wear for it. Volume 2 on the other hand was lightly used today and the binding looks like it isn’t going to hold for long. The pages look like they were printed using a copying machine, looks like a knockoff, very disappointing considering the money you’re spending. Great book but better look elsewhere.

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