Elementary Real and Complex Analysis
(eBook)
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Format
eBook
Language
English
ISBN
9780486135007
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Citations
APA Citation, 7th Edition (style guide)
Georgi E. Shilov., & Georgi E. Shilov|AUTHOR. (2012). Elementary Real and Complex Analysis . Dover Publications.
Chicago / Turabian - Author Date Citation, 17th Edition (style guide)Georgi E. Shilov and Georgi E. Shilov|AUTHOR. 2012. Elementary Real and Complex Analysis. Dover Publications.
Chicago / Turabian - Humanities (Notes and Bibliography) Citation, 17th Edition (style guide)Georgi E. Shilov and Georgi E. Shilov|AUTHOR. Elementary Real and Complex Analysis Dover Publications, 2012.
MLA Citation, 9th Edition (style guide)Georgi E. Shilov, and Georgi E. Shilov|AUTHOR. Elementary Real and Complex Analysis Dover Publications, 2012.
Note! Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy. Citation formats are based on standards as of August 2021.
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Grouping Information
Grouped Work ID | 7ad1fb88-71f6-f5e4-cf3c-b902e6767096-eng |
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Full title | elementary real and complex analysis |
Author | shilov georgi e |
Grouping Category | book |
Last Update | 2024-05-14 23:01:28PM |
Last Indexed | 2024-05-16 00:51:40AM |
Book Cover Information
Image Source | hoopla |
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First Loaded | Feb 9, 2023 |
Last Used | Feb 9, 2023 |
Hoopla Extract Information
stdClass Object ( [year] => 2012 [artist] => Georgi E. Shilov [fiction] => [coverImageUrl] => https://cover.hoopladigital.com/csp_9780486135007_270.jpeg [titleId] => 11603037 [isbn] => 9780486135007 [abridged] => [language] => ENGLISH [profanity] => [title] => Elementary Real and Complex Analysis [demo] => [segments] => Array ( ) [pages] => 544 [children] => [artists] => Array ( [0] => stdClass Object ( [name] => Georgi E. Shilov [relationship] => AUTHOR ) ) [genres] => Array ( [0] => Applied [1] => Mathematics [2] => Number Theory ) [price] => 2.29 [id] => 11603037 [edited] => [kind] => EBOOK [active] => 1 [upc] => [synopsis] => In this book the renowned Russian mathematician Georgi E. Shilov brings his unique perspective to real and complex analysis, an area of perennial interest in mathematics. Although there are many books available on the topic, the present work is specially designed for undergraduates in mathematics, science and engineering. A high level of mathematical sophistication is not required. The book begins with a systematic study of real numbers, understood to be a set of objects satisfying certain definite axioms. The concepts of a mathematical structure and an isomorphism are introduced in Chapter 2, after a brief digression on set theory, and a proof of the uniqueness of the structure of real numbers is given as an illustration. Two other structures are then introduced, namely n-dimensional space and the field of complex numbers. After a detailed treatment of metric spaces in Chapter 3, a general theory of limits is developed in Chapter 4. Chapter 5 treats some theorems on continuous numerical functions on the real line, and then considers the use of functional equations to introduce the logarithm and the trigonometric functions. Chapter 6 is on infinite series, dealing not only with numerical series but also with series whose terms are vectors and functions (including power series). Chapters 7 and 8 treat differential calculus proper, with Taylor's series leading to a natural extension of real analysis into the complex domain. Chapter 9 presents the general theory of Riemann integration, together with a number of its applications. Analytic functions are covered in Chapter 10, while Chapter 11 is devoted to improper integrals, and makes full use of the technique of analytic functions. Each chapter includes a set of problems, with selected hints and answers at the end of the book. A wealth of examples and applications can be found throughout the text. Over 340 theorems are fully proved. [url] => https://www.hoopladigital.com/title/11603037 [pa] => [publisher] => Dover Publications [purchaseModel] => INSTANT )