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  • Introduction to Calculus and Analysis: Volume II

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Introduction to Calculus and Analysis: Volume II

by Richard Courant (Author), Fritz John (Author), Albert A. Blank (Assistant), Format: Hardcover
4.6 out of 5 stars (7)
The new Chapter 1 contains all the fundamental properties of linear differential forms and their integrals. These prepare the reader for the introduction to higher-order exterior differential forms added to Chapter 3. Also found now in Chapter 3 are a new proof of the implicit function theorem by successive approximations and a discus­ sion of numbers of critical points and of indices of vector fields in two dimensions. Extensive additions were made to the fundamental properties of multiple integrals in Chapters 4 and 5. Here one is faced with a familiar difficulty: integrals over a manifold M, defined easily enough by subdividing M into convenient pieces, must be shown to be inde­ pendent of the particular subdivision. This is resolved by the sys­ tematic use of the family of Jordan measurable sets with its finite intersection property and of partitions of unity. In order to minimize topological complications, only manifolds imbedded smoothly into Euclidean space are considered. The notion of "orientation" of a manifold is studied in the detail needed for the discussion of integrals of exterior differential forms and of their additivity properties. On this basis, proofs are given for the divergence theorem and for Stokes's theorem in n dimensions. To the section on Fourier integrals in Chapter 4 there has been added a discussion of Parseval's identity and of multiple Fourier integrals.
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  1. ISBN-10
    0387971521
  2. ISBN-13
    978-0387971520
  3. Edition
    1st ed. 1974. 2nd printing
  4. Publisher
    Springer
  5. Publication date
    October 2, 1989
  6. Language
    English
  7. Dimensions
    6.25 x 2 x 9.5 inches
  8. Print length
    954 pages
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  2. Introduction to Calculus and Analysis, Vol. II/2 (Classics in Mathematics)
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  4. Differential and Integral Calculus, Vol. One
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  5. Differential and Integral Calculus, Vol. 2
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Product details

  • Publisher ‏ : ‎ Springer
  • Publication date ‏ : ‎ October 2, 1989
  • Edition ‏ : ‎ 1st ed. 1974. 2nd printing
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 954 pages
  • ISBN-10 ‏ : ‎ 0387971521
  • ISBN-13 ‏ : ‎ 978-0387971520
  • Item Weight ‏ : ‎ 3.35 pounds
  • Dimensions ‏ : ‎ 6.25 x 2 x 9.5 inches
  • Best Sellers Rank: #4,864,376 in Books (See Top 100 in Books)
  • Customer Reviews:
    4.6 out of 5 stars (7)

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  1. Fritz John

    Fritz John

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  2. Richard Courant

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4.6 out of 5 stars
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  • Cisternas
    5 out of 5 stars
    Courant vol. 2, Analysis
    Reviewed in the United States on January 23, 2012
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    Book in excelent conditions, like new, despite the fact of being 40 years old. Totally Approved.

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    3 out of 5 stars
    http://ck-math.com
    Reviewed in the United States on November 15, 2016
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    It is not that a good book. Most materials in the book can be found in many advanced calculus books.

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