{"id":3703,"date":"2011-12-14T00:46:16","date_gmt":"2011-12-13T22:46:16","guid":{"rendered":"http:\/\/djalil.chafai.net\/blog\/?p=3703"},"modified":"2017-12-16T07:40:08","modified_gmt":"2017-12-16T06:40:08","slug":"integration-by-parts","status":"publish","type":"post","link":"https:\/\/djalil.chafai.net\/blog\/2011\/12\/14\/integration-by-parts\/","title":{"rendered":"Integration by parts"},"content":{"rendered":"<p><a href=\"http:\/\/en.wikipedia.org\/wiki\/Niels_Henrik_Abel\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-3705\" title=\"Niels Henrik Abel\" src=\"\/blog\/wp-content\/uploads\/2011\/12\/abel-300x184.jpg\" alt=\"Niels Henrik Abel\" width=\"300\" height=\"184\" srcset=\"https:\/\/djalil.chafai.net\/blog\/wp-content\/uploads\/2011\/12\/abel-300x184.jpg 300w, https:\/\/djalil.chafai.net\/blog\/wp-content\/uploads\/2011\/12\/abel-1024x628.jpg 1024w, https:\/\/djalil.chafai.net\/blog\/wp-content\/uploads\/2011\/12\/abel.jpg 1031w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p style=\"text-align: justify;\">It is amusing to realize how much the basic concept of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Integration_by_parts\">integration by parts<\/a> is fruitful in mathematics and in mathematical physics. Here are some instances:<\/p>\n<ul>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Summation_by_parts\">Abel transformation<\/a><\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Schwinger%E2%80%93Dyson_equation\">Schwinger-Dyson equation<\/a><\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Malliavin_calculus\">Malliavin calculus<\/a><\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Schwartz_distribution\">Schwartz-Sobolev distributions<\/a><\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Wick%27s_theorem\">Wick calculus<\/a><\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Stokes%27_theorem\">Stockes' theorem<\/a> and <a href=\"http:\/\/en.wikipedia.org\/wiki\/Green%27s_theorem\">Green's theorem<\/a><\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Stein%27s_method\">Chen-Stein method<\/a><\/li>\n<li>Helffer-Sj\u00f6strand formula<\/li>\n<\/ul>\n<p>The quality of these Wikipedia pages is not homogeneous. Feel free to improve them!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is amusing to realize how much the basic concept of integration by parts is fruitful in mathematics and in mathematical physics. Here are some&#8230;<\/p>\n<div class=\"more-link-wrapper\"><a class=\"more-link\" href=\"https:\/\/djalil.chafai.net\/blog\/2011\/12\/14\/integration-by-parts\/\">Continue reading<span class=\"screen-reader-text\">Integration by parts<\/span><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":57},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/3703"}],"collection":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/comments?post=3703"}],"version-history":[{"count":19,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/3703\/revisions"}],"predecessor-version":[{"id":9973,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/3703\/revisions\/9973"}],"wp:attachment":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/media?parent=3703"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/categories?post=3703"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/tags?post=3703"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}