{"id":23980,"date":"2022-08-31T09:25:27","date_gmt":"2022-08-31T01:25:27","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=23980"},"modified":"2022-09-01T10:44:01","modified_gmt":"2022-09-01T02:44:01","slug":"partial-differential-equations-ii-prof-c-k-lin","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/partial-differential-equations-ii-prof-c-k-lin","title":{"rendered":"Partial Differential Equations II | Department of Applied Mathematics Prof. C. K. Lin"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"23980\" class=\"elementor elementor-23980\">\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 elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3742aef4 elementor-widget elementor-widget-breadcrumbs\" data-id=\"3742aef4\" 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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_19495\" 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\t\t\t\t\t<h3 class=\"penci-ibox-title\">Partial Differential Equations II<\/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\" data-tab=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"home-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-home\" 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     <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<\/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\u5c6c\u7814\u7a76\u6240\u7a0b\u5ea6\u7684\u5fae\u5206\u65b9\u7a0b\u8ab2\u7a0b\uff0c\u6388\u8ab2\u504f\u91cd\u65bc\u6578\u5b78\u8207\u7269\u7406\u9593\u7684\u9023\u7d50\uff0c\u4e26\u4e14\u8b93\u5b78\u751f\u85c9\u7531\u6b64\u8ab2\u7a0b\u4e86\u89e3\u76f4\u89c0\u5730PDE\u6982\u5ff5\u3002<br \/><br \/><\/p><p><span style=\"color: #3366ff; font-size: 16px;\">Textbook\uff1a<\/span><span style=\"font-size: 16px;\">Fritz John, Partial Differential Equations (4th Edition), Applied Mathematical Sciences Vol.1 Springer-Verlag 1982.<br \/><\/span><\/p><p>\u00a0<\/p><p><span style=\"color: #ff00ff;\">For perfect learning results, please buy textbooks!<br \/><br \/><\/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\">Instructor(s)<\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a0Department of Applied Mathematics Prof. C. K. Lin<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Course Credits<\/th><td class=\"\u3002\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a03 Credits<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Academic Year<\/th><td bgcolor=\"#EEEEEE\">\u00a097 Academic Year<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Level<\/th><td>\u00a0Master's Students<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Prior Knowledge<\/th><td bgcolor=\"#EEEEEE\">\u00a0Calculus, Advanced Calculus, Linear Algebra, Ordinary differential equation, Complex Analysis and Real analysis<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Related Resources<\/th><td><i><\/i>\u00a0<a href=\"#video\">Course Video<\/a>\u00a0 \u00a0 <a href=\"#syllabus\">Course Syllabus<\/a>\u00a0 \u00a0 <a href=\"#calendar\">Course Calendar<\/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-45\" class=\"tablepress tablepress-id-45\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/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\u4e94\u7ae0 Hyperbolic Equations in Higher Dimensions<br \/>\n5-1 The Wave Equation in n-Dimensional Space<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=24031&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e94\u7ae0 Hyperbolic Equations in Higher Dimensions<br \/>\n5-2 Higher-Order Hyperbolic Equations with Constant Coefficients<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26387&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e94\u7ae0 Hyperbolic Equations in Higher Dimensions<br \/>\n5-3 Symmetric Hyperbolic System<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26393&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516d\u7ae0 Higher-Order Elliptic Equations with Constant Coefficients<br \/>\n6-1 The Fundamental Solution for Odd n<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26399&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516d\u7ae0 Higher-Order Elliptic Equations with Constant Coefficients<br \/>\n6-2 The Dirichlet Problem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26405&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516d\u7ae0 Higher-Order Elliptic Equations with Constant Coefficients<br \/>\n6-3 Sobolev Space<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26411&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e03\u7ae0 Parabolic Equations<br \/>\n7-1 The Heat Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26417&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e03\u7ae0 Parabolic Equations<br \/>\n7-2 The Initial-Value Problem for General Second-Order Parabolic Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26423&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516b\u7ae0 H. Lewys Example of a Linear Equation without Solutions<br \/>\n8-1 Brief introduction of Functional Analysis<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26429&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516b\u7ae0 H. Lewys Example of a Linear Equation without Solutions<br \/>\n8-2 Semigroups of linear operator<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26435&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516b\u7ae0 H. Lewys Example of a Linear Equation without Solutions<br \/>\n8-3 Perturbations and Approximations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26441&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516b\u7ae0 H. Lewys Example of a Linear Equation without Solutions<br \/>\n8-4 The abstract Cauchy Problem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26447&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516b\u7ae0 H. Lewys Example of a Linear Equation without Solutions<br \/>\n8-5 Application to linear partial differential equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26453&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516b\u7ae0 H. Lewys Example of a Linear Equation without Solutions<br \/>\n8-6 Applications to nonlinear partial differential equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26459&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u516b\u7ae0 H. Lewys Example of a Linear Equation without Solutions<br \/>\n8-6 Applications to nonlinear partial differential equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26465&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-45 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\">\u672c\u8ab2\u7a0b\u5c6c\u7814\u7a76\u6240\u7a0b\u5ea6\u7684\u5fae\u5206\u65b9\u7a0b\u8ab2\u7a0b\uff0c\u6388\u8ab2\u504f\u91cd\u65bc\u6578\u5b78\u8207\u7269\u7406\u9593\u7684\u9023\u7d50\uff0c\u4e26\u4e14\u8b93\u5b78\u751f\u85c9\u7531\u6b64\u8ab2\u7a0b\u4e86\u89e3\u76f4\u89c0\u5730PDE\u6982\u5ff5\u3002<\/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=\"#e4d8b0\"><strong> \u7ae0\u7bc0<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong> \u4e3b\u984c\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u7b2c\u4e94\u7ae0<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Hyperbolic Equations in Higher Dimensions<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516d\u7ae0<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\"> Higher-Order Elliptic Equations with Constant Coefficients<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u7b2c\u4e03\u7ae0<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Parabolic Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516b\u7ae0<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\"> H. Lewys Example of a Linear Equation without Solutions<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">Fritz John, Partial Differential Equations (4th Edition), Applied Mathematical Sciences Vol.1 Springer-Verlag 1982. <br \/>A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.<\/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=\"#e4d8b0\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u5e73\u6642\u4f5c\u696d<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">60%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u671f\u4e2d\u5831\u544a<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">20%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u671f\u672b\u5831\u544a<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">20%<\/span><\/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 border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong> \u4e3b\u984c\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u7b2c\u4e94\u7ae0 Hyperbolic Equations in Higher Dimensions<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">5-1 The Wave Equation in n-Dimensional Space <br \/>5-2 Higher-Order Hyperbolic Equations with Constant Coefficients <br \/>5-3 Symmetric Hyperbolic System<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516d\u7ae0 Higher-Order Elliptic Equations with Constant Coefficients<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">6-1 The Fundamental Solution for Odd n <br \/>6-2 The Dirichlet Problem <br \/>6-3 Sobolev Space<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u7b2c\u4e03\u7ae0 Parabolic Equations<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">7-1 The Heat Equation <br \/>7-2 The Initial-Value Problem for General Second-Order Parabolic Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516b\u7ae0 H. Lewys Example of a Linear Equation without Solutions<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">8-1 Brief introduction of Functional Analysis <br \/>8-2 Semigroups of linear operator <br \/>8-3 Perturbations and Approximations <br \/>8-4 The abstract Cauchy Problem <br \/>8-5 Application to linear partial differential equations <br \/>8-6 Applications to nonlinear partial differential equations<\/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 - v3.13.3 - 28-05-2023 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