{"id":24473,"date":"2022-09-01T17:03:04","date_gmt":"2022-09-01T09:03:04","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=24473"},"modified":"2024-11-15T15:02:35","modified_gmt":"2024-11-15T07:02:35","slug":"%e5%81%8f%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e4%b8%80-partial-differential-equations-i-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e6%9e%97%e7%90%a6%e7%84%9c%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%81%8f%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e4%b8%80-partial-differential-equations-i-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e6%9e%97%e7%90%a6%e7%84%9c%e8%80%81%e5%b8%ab","title":{"rendered":"\u504f\u5fae\u5206\u65b9\u7a0b(\u4e00) Partial Differential Equations I | \u61c9\u7528\u6578\u5b78\u7cfb \u6797\u7426\u711c\u8001\u5e2b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"24473\" class=\"elementor elementor-24473\">\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_99638\" 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\">Partial Differential Equations I<\/div>\t\t\t\t\t<h3 class=\"penci-ibox-title\">\u504f\u5fae\u5206\u65b9\u7a0b(\u4e00)<\/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\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M280.37 148.26L96 300.11V464a16 16 0 0 0 16 16l112.06-.29a16 16 0 0 0 15.92-16V368a16 16 0 0 1 16-16h64a16 16 0 0 1 16 16v95.64a16 16 0 0 0 16 16.05L464 480a16 16 0 0 0 16-16V300L295.67 148.26a12.19 12.19 0 0 0-15.3 0zM571.6 251.47L488 182.56V44.05a12 12 0 0 0-12-12h-56a12 12 0 0 0-12 12v72.61L318.47 43a48 48 0 0 0-61 0L4.34 251.47a12 12 0 0 0-1.6 16.9l25.5 31A12 12 0 0 0 45.15 301l235.22-193.74a12.19 12.19 0 0 1 15.3 0L530.9 301a12 12 0 0 0 16.9-1.6l25.5-31a12 12 0 0 0-1.7-16.93z\"><\/path><\/svg>                                                            \n                                                           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24s-10.7 24-24 24-24-10.7-24-24 10.7-24 24-24zm128 368c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">\u8ab2\u7a0b\u7db1\u8981<\/span>                            \n                                                    <\/li>\n                                            <li id=\"calendar\" class=\"inactive eael-tab-item-trigger\" aria-selected=\"false\" data-tab=\"4\" role=\"tab\" tabindex=\"-1\" aria-controls=\"calendar-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-far-calendar-alt\" viewBox=\"0 0 448 512\" 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;\">\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><span style=\"color: #3366ff; font-size: 16px;\">\u8ab2\u7a0b\u7528\u66f8\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><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 \u6797\u7426\u711c\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\">\u00a097\u5b78\u5e74\u5ea6<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u6388\u8ab2\u5c0d\u8c61<\/th><td>\u00a0\u7814\u7a76\u6240\u5b78\u751f<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u9810\u5099\u77e5\u8b58<\/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\">\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-46\" class=\"tablepress tablepress-id-46\">\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\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-1 Introduction<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=24511\">\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\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-2 Examples<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26479\">\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\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-3 Analytic Solution and Approximation methods in a simple example<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26485\">\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\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-4  Quasilinear Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26491\">\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\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-5 The Cauchy Problem for the Quasilinear-linear Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26497\">\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\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-6 Examples<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26515\">\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\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-7 The general first-order equation for a function of two variables<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26521\">\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\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-8 The Cauchy Problem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26527\">\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\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-9 Solutions generated as envelopes<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26533\">\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\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-1 Characteristics for Linear and Quasilinear Second-Order Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26539\">\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\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-2 Propagation of Singularity<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26545\">\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\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-3 The Linear Second-Order Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26551\">\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\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-4 The One-Dimensional Wave Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26557\">\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\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-5 System of First-Order Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26566\">\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\">\u7b2c\u4e8c\u7ae0Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-6 A Quasi-linear System and Simple Waves<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26572\">\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\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-1 Natation of Laurent Schwartz<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26578\">\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\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-2 The Cauchy Problem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26584\">\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\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-3 Real Analytic Functions and the Cauchy-Kowalevski Theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26590\">\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\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-4 The Lagrange-Green Identity<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26601\">\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\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-5 The Uniqueness Theorem of Holmgren<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26607\">\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\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-6 Distribution Solutions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26613\">\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\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-1 Greens Identity, Fundamental Solutions, and Poissons Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26619\">\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\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-2 The Maximal Principle<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26625\">\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\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-3 The Dirichlet Problem, Greens Function, and Poisson Formula<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26639\">\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\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-4 Perrons method<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26645\">\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\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-5 Solution of the Dirichlet Problem by Hilbert-Space Methods<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26651\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-46 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><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\u4e00\u7ae0<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">The Single First-Order Equation<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u4e8c\u7ae0<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\"> Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u7b2c\u4e09\u7ae0<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Characteristic Manifolds and Cauchy Problem<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u56db\u7ae0<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\"> The Laplace Equation<\/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><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\u4e00\u7ae0 The Single First-Order Equation<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1-1 Introduction <br \/>1-2 Examples <br \/>1-3 Analytic Solution and Approximation methods in a simple example <br \/>1-4 Quasilinear Equation <br \/>1-5 The Cauchy Problem for the Quasilinear-linear Equations <br \/>1-6 Examples <br \/>1-7 The general first-order equation for a function of two variables <br \/>1-8 The Cauchy Problem <br \/>1-9 Solutions generated as envelopes<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2-1 Characteristics for Linear and Quasilinear Second-Order Equations <br \/>2-2 Propagation of Singularity <br \/>2-3 The Linear Second-Order Equation <br \/>2-4 The One-Dimensional Wave Equation <br \/>2-5 System of First-Order Equations <br \/>2-6 A Quasi-linear System and Simple Waves<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3-1 Natation of Laurent Schwartz <br \/>3-2 The Cauchy Problem <br \/>3-3 Real Analytic Functions and the Cauchy-Kowalevski Theorem <br \/>3-4 The Lagrange-Green Identity <br \/>3-5 The Uniqueness Theorem of Holmgren <br \/>3-6 Distribution Solutions<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u56db\u7ae0 The Laplace Equation<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">4-1 Greens Identity, Fundamental Solutions, and Poissons Equation <br \/>4-2 The Maximal Principle <br \/>4-3 The Dirichlet Problem, Greens Function, and Poisson Formula <br \/>4-4 Perrons method <br \/>4-5 Solution of the Dirichlet Problem by Hilbert-Space Methods<\/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\" 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