{"id":4411,"date":"2013-12-20T06:05:46","date_gmt":"2013-12-19T21:05:46","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4411"},"modified":"2014-08-01T19:13:24","modified_gmt":"2014-08-01T10:13:24","slug":"taylor-series-for-functions-of-two-or-more-variables","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4411","title":{"rendered":"Taylor series for functions of two or more variables"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><blockquote>\n<p>The ideas involved in Taylor series for functions of one variable can be generalized. For example, the Taylor series for <img src='https:\/\/s0.wp.com\/latex.php?latex=f%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='f(x, y)' title='f(x, y)' class='latex' \/> about x = a, y = b can be written <\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+f%28x%2C+y%29+%3D+f%28a%2C+b%29+%2B+f_x%28a%2C+b%29%28x+-a%29+%2B+f_y%28a%2C+b%29%28y+-b%29%5C%5C%5Cvspace%7B0.2+in%7D+++%5C+%5C+%5C+%2B+%5Cfrac%7B1%7D%7B2%21%7D%5Cbig%5Bf_%7Bxx%7D%28a%2C+b%29%28x+-+a%29%5E2+%2B+2f_%7Bxy%7D%28a%2C+b%29%28x+-+a%29%28y+-+b%29+%2B+f_%7Byy%7D%28a%2C+b%29%28y+-+b%29%5E2%5Cbig%5D+%2B+%5Ccdots&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle f(x, y) = f(a, b) + f_x(a, b)(x -a) + f_y(a, b)(y -b)\\\\\\vspace{0.2 in}   \\ \\ \\ + \\frac{1}{2!}\\big[f_{xx}(a, b)(x - a)^2 + 2f_{xy}(a, b)(x - a)(y - b) + f_{yy}(a, b)(y - b)^2\\big] + \\cdots' title='\\displaystyle f(x, y) = f(a, b) + f_x(a, b)(x -a) + f_y(a, b)(y -b)\\\\\\vspace{0.2 in}   \\ \\ \\ + \\frac{1}{2!}\\big[f_{xx}(a, b)(x - a)^2 + 2f_{xy}(a, b)(x - a)(y - b) + f_{yy}(a, b)(y - b)^2\\big] + \\cdots' class='latex' \/><\/p><\/blockquote>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>The ideas involved in Taylor series for functions of one variable can be generalized. For example, the Taylor  &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4411\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;Taylor series for functions of two or more variables&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4411","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4411","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4411"}],"version-history":[{"count":4,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4411\/revisions"}],"predecessor-version":[{"id":6067,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4411\/revisions\/6067"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}