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Titlebook: Introduction to Calculus and Analysis; Volume II Richard Courant,Fritz John Textbook Dec 2013Latest edition Springer-Verlag New York, Inc.

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書目名稱Introduction to Calculus and Analysis
副標(biāo)題Volume II
編輯Richard Courant,Fritz John
視頻videohttp://file.papertrans.cn/474/473493/473493.mp4
圖書封面Titlebook: Introduction to Calculus and Analysis; Volume II Richard Courant,Fritz John Textbook Dec 2013Latest edition Springer-Verlag New York, Inc.
描述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
出版日期Textbook Dec 2013Latest edition
關(guān)鍵詞Implicit function; integral; manifold
版次1
doihttps://doi.org/10.1007/978-1-4613-8958-3
copyrightSpringer-Verlag New York, Inc. 1989
The information of publication is updating

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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 additi
地板
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Relations Between Surface and Volume Integrals,als along curves, we encounter integrals over curved surfaces. In the present chapter we shall introduce surface integrals and discuss the mutual relations between integrals over manifolds of varying dimensions..
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Textbook Dec 2013Latest editionion 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 m
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Differential Equations,thin the scope of this book. In this chapter, however, starting with further examples from mechanics, we shall give at least a sketch of some of the principles of the subject, making use of the calculus of functions of several variables.
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Vectors, Matrices, Linear Transformations,Vectors in two dimensions have already been studied in Volume I Chapter 4. Geometric concepts in higher dimensions make the use of vectors even more essential. Vectors serve to express many complicated equations concisely in a manner clearly exhibiting those features that do not depend on a particular choice of coordinate systems.
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Calculus of Variations,In the theory of ordinary maxima and minima of a differentiable function .(.…, .)of . independent variables, the necessary condition (pp. 326–7) for the occurrence of an extreme value at a point of the domain of . is ..
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