{"id":386,"date":"2017-11-06T09:01:40","date_gmt":"2017-11-06T09:01:40","guid":{"rendered":"https:\/\/science.sjp.ac.lk\/mat\/?page_id=386"},"modified":"2017-11-07T02:46:10","modified_gmt":"2017-11-07T02:46:10","slug":"functions-of-several-variables","status":"publish","type":"page","link":"https:\/\/science.sjp.ac.lk\/mat\/functions-of-several-variables\/","title":{"rendered":"Functions of Several Variables"},"content":{"rendered":"<p><strong>Course: \u00a0<\/strong>MAT 221 2.0 Functions of Several Variables (<u>Compulsory<\/u>)<\/p>\n<p><strong>Course content:\u00a0<\/strong><\/p>\n<p style=\"text-align: justify\"><strong>Point Sets in Higher Dimensions: <\/strong>The Euclidean Space , Open ball in and Open sets in , Closed set, Adherent Point, Accumulation point of set and Closure of a set, Bounded sets, Bolzano-Weierstrass Theorem; <strong>Functions in Higher Dimensional Space: <\/strong>Linear Functions in Rational Functions in Algebraic Functions in ; <strong>Limit of Functions: <\/strong>Neighbourhoods of a point, Limit point of a set, Algebra of limits, Non-existence of limit; <strong>Continuity of a function: <\/strong>Continuity, Function Continuous on compact sets, Intermediate value theorem; <strong>Partial Derivatives: <\/strong>Partial derivatives, Directional derivatives, Mean Value Theorem; <strong>Differentiability: <\/strong>Total differential, Sufficient condition for differentiability of a function; <strong>Composite Functions: <\/strong>Chain Rules, Homogeneous functions and Euler\u2019s Theorem, Partial derivatives of higher order, Change of Variables, Jacobins and their important properties; <strong>Implicit Functions: <\/strong>Existence Theorem, Functional Equations<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Recommended Readings: <\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Course: \u00a0MAT 221 2.0 Functions of Several Variables (Compulsory) Course content:\u00a0 Point Sets in Higher Dimensions: The Euclidean Space , Open ball in and Open sets in , Closed set, Adherent Point, Accumulation point of set and Closure of a set, Bounded sets, Bolzano-Weierstrass Theorem; Functions in Higher Dimensional Space: Linear Functions in Rational Functions &hellip; <a href=\"https:\/\/science.sjp.ac.lk\/mat\/functions-of-several-variables\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Functions of Several Variables<\/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\/386"}],"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=386"}],"version-history":[{"count":4,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/386\/revisions"}],"predecessor-version":[{"id":483,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/386\/revisions\/483"}],"wp:attachment":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/media?parent=386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}