Analysis: an introduction
This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces,...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2004
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| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (ix, 261 pages) |
| ISBN: | 9780511755163 |
| DOI: | 10.1017/CBO9780511755163 |
Staff View
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| 505 | 8 | |a Introduction -- The real and complex numbers -- Real and complex sequences -- Series -- Power series -- Metric spaces -- Continuous functions -- Calculus -- Some special functions -- Lebesgue measure on the Line -- Lebesgue integration on the line -- Function spaces -- Fourier series -- Applications of Fourier Series -- Ordinary differential equations -- Appendix: The Banach-Tarski paradox | |
| 520 | |a This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics | ||
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Record in the Search Index
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| author | Beals, Richard 1938- |
| author_facet | Beals, Richard 1938- |
| author_role | aut |
| author_sort | Beals, Richard 1938- |
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| building | Verbundindex |
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| contents | Introduction -- The real and complex numbers -- Real and complex sequences -- Series -- Power series -- Metric spaces -- Continuous functions -- Calculus -- Some special functions -- Lebesgue measure on the Line -- Lebesgue integration on the line -- Function spaces -- Fourier series -- Applications of Fourier Series -- Ordinary differential equations -- Appendix: The Banach-Tarski paradox |
| ctrlnum | (ZDB-20-CBO)CR9780511755163 (OCoLC)967686548 (DE-599)BVBBV043943145 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511755163 |
| format | Electronic eBook |
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| id | DE-604.BV043943145 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:19Z |
| institution | BVB |
| isbn | 9780511755163 |
| language | English |
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| oclc_num | 967686548 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (ix, 261 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Beals, Richard 1938- Verfasser aut Analysis an introduction Richard Beals Cambridge Cambridge University Press 2004 1 online resource (ix, 261 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction -- The real and complex numbers -- Real and complex sequences -- Series -- Power series -- Metric spaces -- Continuous functions -- Calculus -- Some special functions -- Lebesgue measure on the Line -- Lebesgue integration on the line -- Function spaces -- Fourier series -- Applications of Fourier Series -- Ordinary differential equations -- Appendix: The Banach-Tarski paradox This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-60047-7 Erscheint auch als Druckausgabe 978-0-521-84072-9 https://doi.org/10.1017/CBO9780511755163 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Beals, Richard 1938- Analysis an introduction Introduction -- The real and complex numbers -- Real and complex sequences -- Series -- Power series -- Metric spaces -- Continuous functions -- Calculus -- Some special functions -- Lebesgue measure on the Line -- Lebesgue integration on the line -- Function spaces -- Fourier series -- Applications of Fourier Series -- Ordinary differential equations -- Appendix: The Banach-Tarski paradox Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Analysis an introduction |
| title_auth | Analysis an introduction |
| title_exact_search | Analysis an introduction |
| title_full | Analysis an introduction Richard Beals |
| title_fullStr | Analysis an introduction Richard Beals |
| title_full_unstemmed | Analysis an introduction Richard Beals |
| title_short | Analysis |
| title_sort | analysis an introduction |
| title_sub | an introduction |
| topic | Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematical analysis Analysis |
| url | https://doi.org/10.1017/CBO9780511755163 |
| work_keys_str_mv | AT bealsrichard analysisanintroduction |