| 000 | 03395nam a22004815i 4500 | ||
|---|---|---|---|
| 001 | 978-3-031-54831-4 | ||
| 003 | DE-He213 | ||
| 005 | 20251030111824.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 240418s2024 sz | s |||| 0|eng d | ||
| 020 |
_a9783031548314 _9978-3-031-54831-4 |
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| 024 | 7 |
_a10.1007/978-3-031-54831-4 _2doi |
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| 050 | 4 | _aQA299.6-433 | |
| 072 | 7 |
_aPBK _2bicssc |
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| 072 | 7 |
_aMAT034000 _2bisacsh |
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| 072 | 7 |
_aPBK _2thema |
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| 100 | 1 |
_aAksoy, Asuman Güven. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _975367 |
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| 245 | 1 | 0 |
_aFundamentals of Real and Complex Analysis _h[electronic resource] / _cby Asuman Güven Aksoy. |
| 250 | _a1st ed. 2024. | ||
| 264 | 1 |
_aCham : _bSpringer Nature Switzerland : _bImprint: Springer, _c2024. |
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| 300 |
_aXIV, 394 p. 126 illus., 8 illus. in color. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aSpringer Undergraduate Mathematics Series, _x2197-4144 |
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| 505 | 0 | _aPreface -- Introductory Analysis -- Real Analysis -- Complex Analysis -- Bibliography.-Index. | |
| 520 | _aThe primary aim of this text is to help transition undergraduates to study graduate level mathematics. It unites real and complex analysis after developing the basic techniques and aims at a larger readership than that of similar textbooks that have been published, as fewer mathematical requisites are required. The idea is to present analysis as a whole and emphasize the strong connections between various branches of the field. Ample examples and exercises reinforce concepts, and a helpful bibliography guides those wishing to delve deeper into particular topics. Graduate students who are studying for their qualifying exams in analysis will find use in this text, as well as those looking to advance their mathematical studies or who are moving on to explore another quantitative science. Chapter 1 contains many tools for higher mathematics; its content is easily accessible, though not elementary. Chapter 2 focuses on topics in real analysis such as p-adic completion, Banach Contraction Mapping Theorem and its applications, Fourier series, Lebesgue measure and integration. One of this chapter’s unique features is its treatment of functional equations. Chapter 3 covers the essential topics in complex analysis: it begins with a geometric introduction to the complex plane, then covers holomorphic functions, complex power series, conformal mappings, and the Riemann mapping theorem. In conjunction with the Bieberbach conjecture, the power and applications of Cauchy’s theorem through the integral formula and residue theorem are presented. | ||
| 650 | 0 |
_aMathematical analysis. _964178 |
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| 650 | 1 | 4 | _aAnalysis. |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031548307 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031548321 |
| 830 | 0 |
_aSpringer Undergraduate Mathematics Series, _x2197-4144 _975368 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-54831-4 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-SXMS | ||
| 999 |
_c59208 _d59208 |
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