{"product_id":"elementary-real-analysis-paperback-9780521098687","title":"Elementary Real Analysis (Paperback \/ softback) 9780521098687","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eElementary Real Analysis\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA large number of examples is included, with hints for the solution of many of them. These will be of particular value to students working on their own.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eH. G. Eggleston (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521098687, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 18 December 2008\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e296 pages\u003cbr\u003e21.6 x 14 x 1.7 cm, 0.37 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 textbook covers all the theoretical aspects of real variable analysis which undergraduates reading mathematics are likely to require during the first two or three years of their course. It is based on lecture courses which the author has given in the universities of Wales, Cambridge and London. The subject is presented rigorously and without padding. Definitions are stated explicitly and the whole development of the subject is logical and self-contained. Complex numbers are used but the complex variable calculus is not. 'Applied analysis', such as differential equations and Fourier series, is not dealt with. A large number of examples is included, with hints for the solution of many of them. These will be of particular value to students working on their own.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Notation and Conventions\u003cbr\u003e Preliminaries\u003cbr\u003e 1. Enumerability and sequences\u003cbr\u003e 2. Bounds for sets of numbers\u003cbr\u003e 3. Bounds for functions and sequences\u003cbr\u003e 4. Limits of the sequences\u003cbr\u003e 5. Monotonic sequences\u003cbr\u003e two important examples \u003cbr\u003e irrational powers of positive real numbers\u003cbr\u003e 6. Upper and lower limits of real sequences: the general principle of convergence\u003cbr\u003e 7. Convergence of series\u003cbr\u003e absolute convergence\u003cbr\u003e 8. Conditional convergence\u003cbr\u003e 9. Rearrangement and multiplication of absolutely convergent series\u003cbr\u003e 10. Double series\u003cbr\u003e 11. Power series\u003cbr\u003e 12. Point set theory\u003cbr\u003e 13. The Bolzano-Weierstrass, Cantor and Heine-Borel theorems\u003cbr\u003e 14. Functions defined over real or complex numbers\u003cbr\u003e 15. Functions of a single real variable\u003cbr\u003e limits and continuity\u003cbr\u003e 16. Monotonic functions\u003cbr\u003e functions of bounded variation\u003cbr\u003e 17. Differentiation\u003cbr\u003e mean-value theorems\u003cbr\u003e 18. The nth mean-value theorem: Taylor's theorem\u003cbr\u003e 19. Convex and concave functions\u003cbr\u003e 20. The elementary transcendental functions\u003cbr\u003e 21. Inequalities\u003cbr\u003e 22 The Riemann integral\u003cbr\u003e 23. Integration and differentiation\u003cbr\u003e 24. The Riemann-Stiltjes integral\u003cbr\u003e 25. Improper integrals\u003cbr\u003e convergence of integrals\u003cbr\u003e 26. Further tests for the convergence of series\u003cbr\u003e 27. Uniform convergence\u003cbr\u003e 28. Functions of two real variables. Continuity and differentiability\u003cbr\u003e Hints on the solution of exercises and answers to exercises\u003cbr\u003e Appendix\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: 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":46006390292760,"sku":"9780521098687","price":34.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521098687i_1f4ceea5-9a47-440b-837d-11b43d2c9d82.jpg?v=1694970675","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/elementary-real-analysis-paperback-9780521098687","provider":"Freshly Printed Books","version":"1.0","type":"link"}