{"id":20073,"date":"2022-08-23T13:43:18","date_gmt":"2022-08-23T05:43:18","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=20073"},"modified":"2024-11-15T15:06:27","modified_gmt":"2024-11-15T07:06:27","slug":"%e5%af%a6%e8%ae%8a%e5%87%bd%e6%95%b8%e8%ab%96%e4%ba%8c-real-analysis-ii-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e5%90%b3%e5%9f%b9%e5%85%83%e8%80%81%e5%b8%ab","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-science\/am\/%e5%af%a6%e8%ae%8a%e5%87%bd%e6%95%b8%e8%ab%96%e4%ba%8c-real-analysis-ii-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e5%90%b3%e5%9f%b9%e5%85%83%e8%80%81%e5%b8%ab","title":{"rendered":"\u5be6\u8b8a\u51fd\u6578\u8ad6(\u4e8c) Real Analysis II | \u61c9\u7528\u6578\u5b78\u7cfb \u5433\u57f9\u5143\u8001\u5e2b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"20073\" class=\"elementor elementor-20073\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-13d70f5a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"13d70f5a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-100 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-373a1db9\" data-id=\"373a1db9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-2c3529c0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2c3529c0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-128cf510\" data-id=\"128cf510\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f3e8fc1 elementor-widget elementor-widget-penci-info-box\" data-id=\"2f3e8fc1\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_93176\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t<div class=\"penci-ibox-stit\">Real Analysis II<\/div>\t\t\t\t\t<h3 class=\"penci-ibox-title\">\u5be6\u8b8a\u51fd\u6578\u8ad6(\u4e8c)<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-76f0aacd elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"76f0aacd\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        <div id=\"eael-advance-tabs-76f0aacd\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"76f0aacd\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                                            <li id=\"home\" class=\"active-default eael-tab-item-trigger\" aria-selected=\"true\" 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xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M148 288h-40c-6.6 0-12-5.4-12-12v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12zm108-12v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm96 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm-96 96v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm-96 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm192 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm96-260v352c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V112c0-26.5 21.5-48 48-48h48V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h128V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h48c26.5 0 48 21.5 48 48zm-48 346V160H48v298c0 3.3 2.7 6 6 6h340c3.3 0 6-2.7 6-6z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/span>                            \n                                                    <\/li>\n                                    <\/ul>\n            <\/div>\n            \n            <div class=\"eael-tabs-content\">\n\t\t        \n                    <div id=\"home-tab\" class=\"clearfix eael-tab-content-item active-default\" data-title-link=\"home-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><style type=\"text\/css\">\n.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/><\/style><\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u672c\u8ab2\u7a0b\u662f\u7531\u00a0<a href=\"https:\/\/www.math.nycu.edu.tw\/\" target=\"_blank\" rel=\"noopener\">\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78\u61c9\u7528\u6578\u5b78\u7cfb<\/a>\u00a0\u63d0\u4f9b\u3002\u00a0<\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">This is the course designed to acquaint the graduate students in the applied mathematics department with basic ideas and tools in modern analysis. This comprises the subjects of real analysis and functional analysis, the analysis developed in the 20th century and after. We will treat real analysis mainly in the first semester and functional analysis in the second. Hopefully, we can lay down a solid foundation for further usage in some other theoretical or applied area. After taking the course, the students are expected to have the general idea on the modern ways to attack the analysis problems.<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">\u8ab2\u7a0b\u7528\u66f8\uff1a<\/span><\/p><ol><li>H. L. Royden, Real analysis, third edition,Macmillan, 1989.<\/li><li>A. Torchinsky, Real variables, Addison-Wesley, 1988.<\/li><li>J. B. Conway, A course in functional analysis, 2nd edition, Springer, 1990<\/li><\/ol><p><span style=\"color: #ff00ff;\">\u70ba\u6c42\u5b78\u7fd2\u6210\u6548\u5b8c\u7f8e\uff0c\u8acb\u8cfc\u8cb7\u8ab2\u672c\uff01<\/span><\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\">\u6388\u8ab2\u8001\u5e2b<\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a0\u61c9\u7528\u6578\u5b78\u7cfb \u5433\u57f9\u5143\u8001\u5e2b<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u8ab2\u7a0b\u5b78\u5206<\/th><td class=\"\u3002\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a03\u5b78\u5206<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u6388\u8ab2\u5e74\u5ea6<\/th><td bgcolor=\"#EEEEEE\">\u00a099\u5b78\u5e74\u5ea6<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u6388\u8ab2\u5c0d\u8c61<\/th><td>\u00a0\u78a9\u58eb\u73ed\u5b78\u751f<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u9810\u5099\u77e5\u8b58<\/th><td bgcolor=\"#EEEEEE\">\u00a0Advanced calculus and general mathematical maturity.<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u8ab2\u7a0b\u63d0\u4f9b<\/th><td><i><\/i>\u00a0<a href=\"#video\">\u8ab2\u7a0b\u5f71\u97f3<\/a>\u00a0 \u00a0\u00a0<a href=\"#syllabus\">\u8ab2\u7a0b\u7db1\u8981<\/a>\u00a0 \u00a0 <a href=\"#calendar\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/a><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-36\" class=\"tablepress tablepress-id-36\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">\u9031\u6b21<\/th><th class=\"column-2\">\u8ab2\u7a0b\u5167\u5bb9<\/th><th class=\"column-3\">\u8ab2\u7a0b\u5f71\u97f3<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Metric spaces<br \/>\nClass36<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=20100\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class37<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22680\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class38<br \/>\nSec3.4 Complete metric spaces<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22686\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class39<br \/>\nSec3.5 Compact metric spaces<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22695\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class40<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22701\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class41<br \/>\nSec3.7 Stone-Weierstiass Thm.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22707\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class42-43<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22713\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u56db\u7ae0 Banach spaces<br \/>\nClass44<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22719\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class45<br \/>\nSec. 4.2 Subspace &amp; bases<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22725\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class46<br \/>\nSec. 4.4 Linear Transformations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22731\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">class47<br \/>\nSec. 4.5 Principle of uniform bddness (Banach- Steinhaus Thm)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22737\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class48<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22743\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class49<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22749\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class50<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22755\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class51<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22761\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class52<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22767\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class53<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22773\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class54-55<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22779\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class56<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22785\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class57<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22791\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class58<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22797\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class59<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22803\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class60-61<br \/>\nSec. 4.13 Adjoint operators<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22809\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class62<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22815\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class63<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22821\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class64-65<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22827\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class66<br \/>\nsec. 5.2 Fredholm-Riesz-Schauder Theory<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22833\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class67<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22839\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class68<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22845\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Class69<br \/>\nSec.5.3 Spectral theory<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=22851\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-36 from cache --><\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>\u8ab2\u7a0b\u76ee\u6a19<\/strong><\/p><p class=\"text\">This is the course designed to acquaint the graduate students in the applied mathematics department with basic ideas and tools in modern analysis. This comprises the subjects of real analysis and functional analysis, the analysis developed in the 20th century and after. We will treat real analysis mainly in the first semester and functional analysis in the second. Hopefully, we can lay down a solid foundation for further usage in some other theoretical or applied area. After taking the course, the students are expected to have the general idea on the modern ways to attack the analysis problems.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u7ae0\u7bc0<\/strong><\/p><p>\u00a0<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong> \u55ae\u5143\u4e3b\u984c<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong> \u5167\u5bb9\u7db1\u8981<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Functional analysis in Banach spaces<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Principle of uniform boundedness, open mapping theorem, closed graph theorem, Hahn-Banach theorem, completeness of Lp-spaces<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Compact operators<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Fredholm-Riesz-Schauder theory for compact operators<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Spectral theory of self-adjoint operators<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Self-adjoint operators, normal operators\u3000<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Hilbert spaces<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Basic properties of Hilbert spaces<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">H. L. Royden, Real analysis, third edition,Macmillan, 1989. <br \/>A. Torchinsky, Real variables, Addison-Wesley, 1988. <br \/>J. B. Conway, A course in functional analysis, 2nd edition, Springer, 1990.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8a55\u5206\u6a19\u6e96<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u4f5c\u696d<\/span><\/td><td style=\"padding: 5px;\">1\/3<\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u671f\u4e2d\u8003<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\">1\/3<\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u671f\u672b\u8003<\/span><\/td><td style=\"padding: 5px;\">1\/3<\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"calendar-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"calendar-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4; font-size: 15px;\">\u672c\u8ab2\u7a0b\u884c\u4e8b\u66c6\u63d0\u4f9b\u8ab2\u7a0b\u9032\u5ea6\u8207\u8003\u8a66\u8cc7\u8a0a\u53c3\u8003\u3002<\/span><\/p><p>\u00a0<\/p><table style=\"font-style: normal; line-height: 20px; font-size: 15px; text-align: center;\" border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong> \u55ae\u5143\u4e3b\u984c<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong> \u5167\u5bb9\u7db1\u8981<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Functional analysis in Banach spaces<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Principle of uniform boundedness, open mapping theorem, closed graph theorem, Hahn-Banach theorem, completeness of Lp-spaces<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Compact operators<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Fredholm-Riesz-Schauder theory for compact operators<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Spectral theory of self-adjoint operators<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Self-adjoint operators, normal operators\u3000<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Hilbert spaces<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Basic properties of Hilbert spaces<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t                    <\/div>\n        <\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-44bdbd33 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"44bdbd33\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - 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