{"product_id":"lectures-on-real-analysis-hardback-9781107026780","title":"Lectures on Real Analysis (Hardback) 9781107026780","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLectures on Real Analysis\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA rigorous introduction to real analysis for undergraduates. Concise yet comprehensive, it includes a gentle introduction to metric spaces.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eFinnur Lárusson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107026780, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 7 June 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e128 pages, 200 exercises\u003cbr\u003e23.4 x 15.5 x 1.3 cm, 0.32 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e To the student\u003cbr\u003e 1. Numbers, sets, and functions\u003cbr\u003e 2. The real numbers\u003cbr\u003e 3. Sequences\u003cbr\u003e 4. Open, closed, and compact sets\u003cbr\u003e 5. Continuity\u003cbr\u003e 6. Differentiation\u003cbr\u003e 7. Integration\u003cbr\u003e 8. Sequences and series of functions\u003cbr\u003e 9. Metric spaces\u003cbr\u003e 10. The contraction principle\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Trigonometry [\u003ca title=\"See our other books on Trigonometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Trigonometry%20%5BPBMB%5D%22\"\u003ePBMB\u003c\/a\u003e], Differential calculus \u0026amp; equations [\u003ca title=\"See our other books on Differential calculus \u0026amp; equations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Differential%20calculus%20\u0026amp;%20equations%20%5BPBKJ%5D%22\"\u003ePBKJ\u003c\/a\u003e], Real analysis, real variables [\u003ca title=\"See our other books on Real analysis, real variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Real%20analysis,%20real%20variables%20%5BPBKB%5D%22\"\u003ePBKB\u003c\/a\u003e], Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265509806360,"sku":"9781107026780","price":123.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107026780i.jpg?v=1692023628","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/lectures-on-real-analysis-hardback-9781107026780","provider":"Freshly Printed Books","version":"1.0","type":"link"}