{"id":351,"date":"2018-12-26T04:49:42","date_gmt":"2018-12-26T04:49:42","guid":{"rendered":"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=351"},"modified":"2018-12-26T04:53:01","modified_gmt":"2018-12-26T04:53:01","slug":"mathematical-preliminaries-viii","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/chapter\/mathematical-preliminaries-viii\/","title":{"rendered":"Mathematical Preliminaries VIII"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/pd0_cUlppd4\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"alignnone size-full wp-image-353\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2.jpg\" alt=\"\" width=\"1401\" height=\"1717\" \/> <img class=\"alignnone size-full wp-image-354\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3.jpg\" alt=\"\" width=\"1433\" height=\"1751\" \/> <img class=\"alignnone size-full wp-image-355\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4.jpg\" alt=\"\" width=\"1433\" height=\"1673\" \/> <img class=\"alignnone size-full wp-image-356\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5.jpg\" alt=\"\" width=\"1419\" height=\"1715\" \/> <img class=\"alignnone size-full wp-image-357\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6.jpg\" alt=\"\" width=\"1401\" height=\"1577\" \/>\r\n\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Mathematical Preliminaries VIII<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/pd0_cUlppd4\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/pd0_cUlppd4\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<br \/>\n&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-353\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2.jpg\" alt=\"\" width=\"1401\" height=\"1717\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2.jpg 1401w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2-245x300.jpg 245w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2-768x941.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2-836x1024.jpg 836w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2-65x80.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2-225x276.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-2-350x429.jpg 350w\" sizes=\"auto, (max-width: 1401px) 100vw, 1401px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-354\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3.jpg\" alt=\"\" width=\"1433\" height=\"1751\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3.jpg 1433w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3-246x300.jpg 246w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3-768x938.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3-838x1024.jpg 838w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3-65x79.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3-225x275.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-3-350x428.jpg 350w\" sizes=\"auto, (max-width: 1433px) 100vw, 1433px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-355\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4.jpg\" alt=\"\" width=\"1433\" height=\"1673\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4.jpg 1433w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4-257x300.jpg 257w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4-768x897.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4-877x1024.jpg 877w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4-65x76.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4-225x263.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-4-350x409.jpg 350w\" sizes=\"auto, (max-width: 1433px) 100vw, 1433px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-356\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5.jpg\" alt=\"\" width=\"1419\" height=\"1715\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5.jpg 1419w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5-248x300.jpg 248w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5-768x928.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5-847x1024.jpg 847w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5-65x79.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5-225x272.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-5-350x423.jpg 350w\" sizes=\"auto, (max-width: 1419px) 100vw, 1419px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-357\" src=\"http:\/\/statp05.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6.jpg\" alt=\"\" width=\"1401\" height=\"1577\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6.jpg 1401w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6-267x300.jpg 267w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6-768x864.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6-910x1024.jpg 910w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6-65x73.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6-225x253.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-content\/uploads\/sites\/130\/2018\/12\/9610_et_ltext9-6-350x394.jpg 350w\" sizes=\"auto, (max-width: 1401px) 100vw, 1401px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Mathematical Preliminaries VIII<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/pd0_cUlppd4\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"author":3,"menu_order":29,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-rahul-bhattacharya"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-351","chapter","type-chapter","status-publish","hentry","contributor-prof-rahul-bhattacharya"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/pressbooks\/v2\/chapters\/351","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":3,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/pressbooks\/v2\/chapters\/351\/revisions"}],"predecessor-version":[{"id":359,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/pressbooks\/v2\/chapters\/351\/revisions\/359"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/pressbooks\/v2\/chapters\/351\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/wp\/v2\/media?parent=351"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/pressbooks\/v2\/chapter-type?post=351"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/wp\/v2\/contributor?post=351"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp05\/wp-json\/wp\/v2\/license?post=351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}