{"id":438,"date":"2017-11-06T10:05:37","date_gmt":"2017-11-06T10:05:37","guid":{"rendered":"https:\/\/science.sjp.ac.lk\/mat\/?page_id=438"},"modified":"2024-12-19T03:40:45","modified_gmt":"2024-12-19T03:40:45","slug":"real-analysis-ii","status":"publish","type":"page","link":"https:\/\/science.sjp.ac.lk\/mat\/real-analysis-ii\/","title":{"rendered":"Real Analysis II"},"content":{"rendered":"<section class=\"wpb-content-wrapper\"><p>[vc_row][vc_column][vc_column_text]<strong>Course:<\/strong>\u00a0 MAT 376 3.0 Real Analysis II (Compulsory)<\/p>\n<p style=\"text-align: justify;\"><strong>Course Content<\/strong>: <strong>Properties of the real numbers: <\/strong><\/p>\n<p style=\"text-align: justify;\">Set theoretic preliminaries, Real number system as a complete ordered field, Sequences of real numbers, Subsequences, Bounded and monotone sequences, Convergence and the Cauchy criterion, Limit superior and limit inferior for sequences, Some special sequences, Series of real numbers, Serries convergence, Absolute and conditional convergence, tests for convergence, Rearrangements of series, Real functions, Boundedness and monotonicity, Limits and continuity at a point,\u00a0 Continuity on an interval, Intermediate value theorem andextreme value theorem, Uniform continuity, Limits at infinity and infinite limits, Differentiability and the derivative of a real function, Rolle\u2019s and mean value theorems, Higher order derivatives, Sequences and series of functions, Uniform and point-wise convergence, Weierstrass M-test, Uniform convergence and continuity, Uniform convergence and differentiability, Power series and radius of convergence, Exponential and logarithmic functions, Trigonometric functions.<\/p>\n<p><strong>Recommend Readings:<\/strong><\/p>\n<ol>\n<li>Rudin, W., <em>The Principles of Mathematical Analysis,<\/em> 3<sup>rd<\/sup> International Series in Pure &amp; Applied Mathematics, 2006<\/li>\n<li>Bartle, R. G., &amp; Sherbert, D. R., <em>Introduction to Real Analysis,<\/em> 4<sup>th<\/sup> Wiley 2011<\/li>\n<li>Gooldberg, R. T., <em>Methods of Real Analysis<\/em>, 2<sup>nd<\/sup> Wiley, 1976<\/li>\n<li>Pugh, C. C.,<em> Real Mathematical Analysis<\/em>, 2<sup>nd<\/sup> Undergraduate Texts in Mathematics, 2015<\/li>\n<li>Mattuck, A., <em>Introduction to Analysis<\/em>, Illustrated ed. Prentice Hall, 1999<\/li>\n<li>Hammack, R., <em>BOOK OF PROOF<\/em>, 3<sup>rd<\/sup> Richard Hammack, 2018 (<u><a href=\"https:\/\/www.people.vcu.edu\/~rhammack\/BookOfProof\/\">https:\/\/www.people.vcu.edu\/~rhammack\/BookOfProof\/<\/a><\/u>)<\/li>\n<\/ol>\n<p>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n<\/section>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text]Course:\u00a0 MAT 376 3.0 Real Analysis II (Compulsory) Course Content: Properties of the real numbers: Set theoretic preliminaries, Real number system as a complete ordered field, Sequences of real numbers, Subsequences, Bounded and monotone sequences, Convergence and the Cauchy criterion, Limit superior and limit inferior for sequences, Some special sequences, Series of real numbers, Serries &hellip; <a href=\"https:\/\/science.sjp.ac.lk\/mat\/real-analysis-ii\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Real Analysis II<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/438"}],"collection":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/comments?post=438"}],"version-history":[{"count":3,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/438\/revisions"}],"predecessor-version":[{"id":4691,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/438\/revisions\/4691"}],"wp:attachment":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/media?parent=438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}