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140122 ||| eng |
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|a 9781461230243
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| 100 |
1 |
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|a Berenstein, Carlos A.
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| 245 |
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|a Complex Variables
|h Elektronische Ressource
|b An Introduction
|c by Carlos A. Berenstein, Roger Gay
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| 250 |
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|a 1st ed. 1991
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| 260 |
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|a New York, NY
|b Springer New York
|c 1991, 1991
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| 300 |
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|a XII, 652 p
|b online resource
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| 505 |
0 |
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|a 1 Topology of the Complex Plane and Holomorphic Functions -- 1.1. Some Linear Algebra and Differential Calculus -- 1.2. Differential Forms on an Open Subset ? of ? -- 1.3. Partitions of Unity -- 1.4, Regular Boundaries -- 1.5. Integration of Differential Forms of Degree 2. The Stokes Formula -- 1.6. Homotopy. Fundamental Group -- 1.7. Integration of Closed 1-Forms Along Continuous Paths -- 1.8. Index of a Loop -- 1.9. Homology -- 1.10. Residues -- 1.11. Holomorphic Functions -- 2 Analytic Properties of Holomorphic Functions -- 2.1. Integral Representation Formulas -- 2.2. The Frechet Space ? (?) -- 2,3. Holomorphic Maps -- 2.4. Isolated Singularities and Residues -- 2.5. Residues and the Computation of Definite Integrals -- 2.6. Other Applications of the Residue Theorem -- 2.7, The Area Theorem -- 2.8. Conformal Mappings -- 3 The
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| 653 |
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|a Mathematical analysis
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| 653 |
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|a Analysis
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| 700 |
1 |
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|a Gay, Roger
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Graduate Texts in Mathematics
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| 028 |
5 |
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|a 10.1007/978-1-4612-3024-3
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| 856 |
4 |
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|u https://doi.org/10.1007/978-1-4612-3024-3?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515
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| 520 |
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|a Textbooks, even excellent ones, are a reflection of their times. Form and content of books depend on what the students know already, what they are expected to learn, how the subject matter is regarded in relation to other divisions of mathematics, and even how fashionable the subject matter is. It is thus not surprising that we no longer use such masterpieces as Hurwitz and Courant's Funktionentheorie or Jordan's Cours d'Analyse in our courses. The last two decades have seen a significant change in the techniques used in the theory of functions of one complex variable. The important role played by the inhomogeneous Cauchy-Riemann equation in the current research has led to the reunification, at least in their spirit, of complex analysis in one and in several variables. We say reunification since we think that Weierstrass, Poincare, and others (in contrast to many of our students) did not consider them to be entirely separate subjects. Indeed, not only complex analysis in several variables, but also number theory, harmonic analysis, and other branches of mathematics, both pure and applied, have required a reconsidera tion of analytic continuation, ordinary differential equations in the complex domain, asymptotic analysis, iteration of holomorphic functions, and many other subjects from the classic theory of functions of one complex variable. This ongoing reconsideration led us to think that a textbook incorporating some of these new perspectives and techniques had to be written
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