{"id":29373,"date":"2022-09-14T14:46:17","date_gmt":"2022-09-14T06:46:17","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=29373"},"modified":"2024-11-15T14:59:10","modified_gmt":"2024-11-15T06:59:10","slug":"%e5%81%8f%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%b0%8e%e8%ab%96-introduction-to-partial-differential-equations-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e6%9d%8e%e6%a6%ae%e8%80%80%e8%80%81","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%e5%b0%8e%e8%ab%96-introduction-to-partial-differential-equations-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e6%9d%8e%e6%a6%ae%e8%80%80%e8%80%81","title":{"rendered":"\u504f\u5fae\u5206\u65b9\u7a0b\u5c0e\u8ad6 Introduction to Partial Differential Equations | \u61c9\u7528\u6578\u5b78\u7cfb \u674e\u69ae\u8000\u8001\u5e2b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"29373\" class=\"elementor elementor-29373\">\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-90a0113 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"90a0113\" 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-78bf394\" data-id=\"78bf394\" 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-0025485 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0025485\" 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-0446ed9\" data-id=\"0446ed9\" 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-2f5840a elementor-widget elementor-widget-penci-info-box\" data-id=\"2f5840a\" 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_31615\" 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\">Introduction to Partial Differential Equations<\/div>\t\t\t\t\t<h3 class=\"penci-ibox-title\">\u504f\u5fae\u5206\u65b9\u7a0b\u5c0e\u8ad6<\/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-c6381f4 elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"c6381f4\" 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-c6381f4\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"c6381f4\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                      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24zm96-192c13.3 0 24 10.7 24 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 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                            \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>\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;\">Mathematical models as PDE \u2500 qualitative and quantative analysis.<br \/>Three classical types of linear PDEs and the corresponding theory.<br \/>A short topic on nonlinear PDE.<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">\u8ab2\u7a0b\u7528\u66f8\uff1a<\/span><\/p><p><span style=\"font-size: 16px;\">PDE, An Introduction, 2nd ed. by Walter A. Strauss;Publisher: Wiley<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\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u6559\u5e2b<\/span><\/span><\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u61c9\u7528\u6578\u5b78\u7cfb \u674e\u69ae\u8000\u8001\u5e2b<\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u8ab2\u7a0b\u5b78\u5206<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03\u5b78\u5206<\/span><\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u5e74\u5ea6<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0103\u5b78\u5e74\u5ea6<\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u5c0d\u8c61<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u5927\u5b78\u4e8c\u5e74\u7d1a\u5b78\u751f<\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u9810\u5099\u77e5\u8b58<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u5e38\u5fae\u5206\u65b9\u7a0b (Differential Equations)<\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u8ab2\u7a0b\u63d0\u4f9b<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0<a href=\"#video\">\u8ab2\u7a0b\u5f71\u97f3<\/a>\u00a0 \u00a0<a href=\"#syllabus\">\u8ab2\u7a0b\u7db1\u8981<\/a> \u00a0\u00a0<a href=\"#calendar\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/a><\/span><\/span><\/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-66\" class=\"tablepress tablepress-id-66\">\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\">\u7b2c\u4e00\u9031<\/td><td class=\"column-2\">PDE\u5c0e\u8ad6.<br \/>\nFundamental differences between PDE and ODE.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=29440\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e8c\u9031<\/td><td class=\"column-2\">First and second order linear wave equations;<br \/>\nTransport equations<br \/>\nCharacteristic lines;<br \/>\nTravelling wave solutions.<br \/>\nWave equations with dispersion, dissipation, and nonlinearity.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32671\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">\u7b2c\u4e8c\u9031<\/td><td class=\"column-2\">Classical linear wave equations with travelling wave solutions.<br \/>\nDispersive linear wave equations.<br \/>\nDissipative linear wave equations.<br \/>\nNonlinear wave equations with shock wave solutions.<br \/>\nNonlinear wave equations with solitary wave solutions.<br \/>\nInitial value p<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32703\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e09\u9031<\/td><td class=\"column-2\">Classification of 3 types of second order linear PDEs (I).<br \/>\nInitial value problem for a whole-line linear wave equation and the dAlembert solutions (II).<br \/>\nInitial-boundary value problem for a half-line linear wave equation.<br \/>\nInitial-boundary value problem fo<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32709\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\">\u7b2c\u56db\u9031<\/td><td class=\"column-2\">Initial-boundary value problem for a finite-line linear wave equation (II).<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32715\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e94\u9031<\/td><td class=\"column-2\">Linear superposition and sub-problems.<br \/>\nMethod of Separation of Variables.<br \/>\nFourier series representations of solutions.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32721\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">\u7b2c\u516d\u9031<\/td><td class=\"column-2\">Classification of 3 types of second order linear PDEs (II).<br \/>\nInitial value problem for a whole-line linear heat equation solved by the Fundamental solution.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32727\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e03\u9031<\/td><td class=\"column-2\">Initial-boundary value problem for a finite-line linear heat equations solved by method of Separation of Variables.<br \/>\nInitial value problem for an infinite-line linear heat equation solved by Fourier transform and inverse Fourier transform.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32733\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">\u7b2c\u516b\u9031<\/td><td class=\"column-2\">Boundary value problem for a Laplace\u2019s equation in a rectangle solved by method of Separation of Variables.<br \/>\nBoundary value problem for a Laplace\u2019s equation in a circle solved by method of Separation of Variables.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32739\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e5d\u9031<\/td><td class=\"column-2\">Boundary value problem for a Poisson\u2019s equation in a circle.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32748\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u9031<\/td><td class=\"column-2\">Well-posed problems for linear PDE systems (I).<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32756\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e00\u9031<\/td><td class=\"column-2\">Well-posed problems for linear PDE systems (II).<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32767\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e8c\u9031<\/td><td class=\"column-2\">Well-posed problems for linear PDE systems (III).<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32773\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e09\u9031<\/td><td class=\"column-2\">Nonlinear problems (I) -<br \/>\nThe effect of a combination of nonlinearity and dispersion;<br \/>\nThe effect of a combination of nonlinearity and dissipation;<br \/>\nThe effect of a combination of nonlinearity, dispersion, and dissipation.<br \/>\n<br \/>\nShock waves, steady-state solution<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32781\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u56db\u9031<\/td><td class=\"column-2\">Nonlinear problems (II) - kdV equation and the solitary solutions.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32787\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e94\u9031<\/td><td class=\"column-2\">Nonlinear Problems (III) - : Three famous universal nonlinear PDEs - kdV, s-G, and NLS equations.<br \/>\nCompletely integrable systems.<br \/>\ns-G equation and the travelling wave solutions.<br \/>\nNLS equation and the solitary wave solutions.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32793\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u516d\u9031<\/td><td class=\"column-2\">Nonlinear Problems (IV) - Introduction of Riemann surfaces of genus N (1) for the underlying theory of solutions of universal nonlinear PDEs such as kdV, s-G, and NLS.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32799\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e03\u9031<\/td><td class=\"column-2\">Nonlinear Problems (V) - Introduction of Riemann surfaces of genus N (2) for the underlying theory of solutions of universal nonlinear PDEs such as kdV, s-G, and NLS.<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32805\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-66 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\">Mathematical models as PDE \u2013 qualitative and quantative analysis. <br \/>Three classical types of lineat PDEs and the corresponding theory. <br \/>A short topics on nonlinear PDE.<\/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> \u7ae0\u7bc0\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">PDE\u5c0e\u8ad6 <br \/>Fundamental differences between PDE and ODE.<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1.1* What is a Partial Differential Equation? <br \/>1.2* First-Order Linear Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">First and second order linear wave equations; <br \/>Transport equations <br \/>Characteristic lines; <br \/>Travelling wave solutions. <br \/>Wave equations with dispersion, dissipation, and nonlinearity<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.1* The Wave Equation<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Classical linear wave equations with travelling wave solutions. <br \/>Dispersive linear wave equations. <br \/>Dissipative linear wave equations. <br \/>Nonlinear wave equations with shock wave solutions. <br \/>Nonlinear wave equations with solitary wave solutions. <br \/>Initial value problem for a whole-line linear wave equation and the dAlembert solution (I)<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1.1* What is a Partial Differential Equation? <br \/>2.1* The Wave Equation <br \/>Supplement to lecture notes\u3000<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Classification of 3 types of second order linear PDEs (I). <br \/>Initial value problem for a whole-line linear wave equation and the dAlembert solutions (II). <br \/>Initial-boundary value problem for a half-line linear wave equation. <br \/>Initial-boundary value problem for a finite-line linear wave equation (I) \u2013 method of Reflection and method of Separation of Variables.<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.1* The Wave Equation <br \/>3.2 Reflections of Waves <br \/>1.6 Types of Second-Order Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Initial-boundary value problem for a finite-line linear wave equation (II).<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3.2 Reflections of Waves <br \/>Supplement to lecture notes<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Linear superposition and sub-problems <br \/>Method of Separation of Variables <br \/>Fourier series representations of solutions<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">4.1* Separation of Variables, The Dirichlet Condition <br \/>Chapter 5 Fourier Series<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Classification of 3 types of second order linear PDEs (II). <br \/>Initial value problem for a whole-line linear heat equation solved by the Fundamental solution<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">2.4* Diffusion on the Whole Line <br \/>4.1* Separation of Variables, The Dirichlet Condition<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Initial-boundary value problem for a finite-line linear heat equations solved by method of Separation of Variables. <br \/>Initial value problem for an infinite-line linear heat equation solved by Fourier transform and inverse Fourier transform.<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">4.1* Separation of Variables, The Dirichlet Condition <br \/>Chapter 5 Fourier Series <br \/>12.3 Fourier Transform<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Boundary value problem for a Poisson\u2019s equation in a circle.<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">6.3* Poisson\u2019s Formula <br \/>Chapter 5 Fourier Series<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Well-posed problems for linear PDE systems (I).<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.5 Well-Posed Problems <br \/>6.1* Laplace\u2019s Equation<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Well-posed problems for linear PDE systems (II).<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1.5 Well-Posed Problems <br \/>6.3* Poisson\u2019s Formula<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Well-posed problems for linear PDE systems (III).<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.1* The Wave Equation<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Nonlinear problems (I) - <br \/>The effect of a combination of nonlinearity and dispersion; <br \/>The effect of a combination of nonlinearity and dissipation; <br \/>The effect of a combination of nonlinearity, dispersion, and dissipation. <br \/>Shock waves, steady-state solutions, travelling wave solutions, soliton solutions, N-soliton solutions, and wavetrains.<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">14.1 Shock Waves <br \/>14.2 Solitary waves and Solitons <br \/>Supplement to lecture notes<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Nonlinear problems (II) - <br \/>kdV equation and the solitary solutions<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">14.1 Shock Waves <br \/>14.2 Solitary waves and Solitons <br \/>Supplement to lecture notes<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Nonlinear Problems (III) - : Three famous universal nonlinear PDEs - kdV, s-G, and NLS equations. <br \/>Completely integrable systems s-G equation and the travelling wave solutions. <br \/>NLS equation and the solitary wave solutions.<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">14.2 Solitary waves and Solitons <br \/>Supplement to lecture notes<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Nonlinear Problems (IV) - Introduction of Riemann surfaces of genus N (1) for the underlying theory of solutions of universal nonlinear PDEs such as kdV, s-G, and NLS.<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Supplement to lecture notes - Extension I of sec14.2 - the underlying theory of solutions of universal nonlinear PDEs (KdV, s-G, and NLS)<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Nonlinear Problems (V) - Introduction of Riemann surfaces of genus N (2) for the underlying theory of solutions of universal nonlinear PDEs such as kdV, s-G, and NLS.<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Supplement to lecture notes - Extension II of sec14-the underlying theory of solutions of universal nonlinear PDEs (KdV, s-G, and NLS)<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">PDE, An Introduction, 2nd ed. by Walter A. Strauss<\/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\">\u56db\u6b21\u8003\u8a66(\u6700\u4f733\u6b21\u6bcf\u6b2130%\uff0c\u5269\u99181\u6b2110%)<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">100%<\/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 style=\"font-style: normal; line-height: 20px; font-size: 15px; text-align: center;\" border=\"1\" cellspacing=\"0\"><tbody><tr><td bgcolor=\"#e4d8b0\" width=\"76\"><div style=\"text-align: center;\"><span style=\"color: #000000; font-weight: bold;\"><strong>\u6388\u8ab2\u65e5\u671f<\/strong><\/span><\/div><\/td><td bgcolor=\"#e4d8b0\" width=\"135\"><div style=\"text-align: center; padding: 5px;\" align=\"center\"><span style=\"font-family: 'Times New Roman'; font-weight: bold;\"><strong>\u4e0a\u8ab2\u65e5\u671f<\/strong><\/span><\/div><\/td><td bgcolor=\"#e4d8b0\" width=\"440\"><div style=\"text-align: center; font-size: 15px; font-weight: bold;\"><strong>\u53c3\u8003\u8ab2\u7a0b\u9032\u5ea6<\/strong><\/div><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><p><span class=\"text\">2015\/02\/25<\/span><\/p><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">PDE\u5c0e\u8ad6 <br \/>Fundamental differences between PDE and ODE.<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">1.1* What is a Partial Differential Equation? <br \/>1.2* First-Order Linear Equations<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2015\/03\/02<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">First and second order linear wave equations; <br \/>Transport equations <br \/>Characteristic lines; <br \/>Travelling wave solutions. <br \/>Wave equations with dispersion, dissipation, and nonlinearity<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.1* The Wave Equation<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/03\/04<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Classical linear wave equations with travelling wave solutions. <br \/>Dispersive linear wave equations. <br \/>Dissipative linear wave equations. <br \/>Nonlinear wave equations with shock wave solutions. <br \/>Nonlinear wave equations with solitary wave solutions. <br \/>Initial value problem for a whole-line linear wave equation and the dAlembert solution (I)<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">1.1* What is a Partial Differential Equation? <br \/>2.1* The Wave Equation <br \/>Supplement to lecture notes\u3000<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2015\/03\/11<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Classification of 3 types of second order linear PDEs (I). <br \/>Initial value problem for a whole-line linear wave equation and the dAlembert solutions (II). <br \/>Initial-boundary value problem for a half-line linear wave equation. <br \/>Initial-boundary value problem for a finite-line linear wave equation (I) \u2013 method of Reflection and method of Separation of Variables.<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.1* The Wave Equation <br \/>3.2 Reflections of Waves <br \/>1.6 Types of Second-Order Equations<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/03\/18<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Initial-boundary value problem for a finite-line linear wave equation (II).<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">3.2 Reflections of Waves <br \/>Supplement to lecture notes<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2015\/03\/25<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Linear superposition and sub-problems <br \/>Method of Separation of Variables <br \/>Fourier series representations of solutions<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">4.1* Separation of Variables, The Dirichlet Condition <br \/>Chapter 5 Fourier Series<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/04\/01<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Classification of 3 types of second order linear PDEs (II). <br \/>Initial value problem for a whole-line linear heat equation solved by the Fundamental solution<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">2.4* Diffusion on the Whole Line <br \/>4.1* Separation of Variables, The Dirichlet Condition<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2015\/04\/08<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Initial-boundary value problem for a finite-line linear heat equations solved by method of Separation of Variables. <br \/>Initial value problem for an infinite-line linear heat equation solved by Fourier transform and inverse Fourier transform.<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">4.1* Separation of Variables, The Dirichlet Condition <br \/>Chapter 5 Fourier Series <br \/>12.3 Fourier Transform<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/04\/15<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Boundary value problem for a Laplace\u2019s equation in a rectangle solved by method of Separation of Variables. <br \/>Boundary value problem for a Laplace\u2019s equation in a circle solved by method of Separation of Variables.<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">6.1* Laplace\u2019s Equation <br \/>6.2* Rectangles and Cubes 161 <br \/>6.3* Poisson\u2019s Formula Chapter 5 Fourier Series<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/04\/22<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Boundary value problem for a Poisson\u2019s equation in a circle.<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">6.3* Poisson\u2019s Formula <br \/>Chapter 5 Fourier Series<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2015\/04\/29<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Well-posed problems for linear PDE systems (I).<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.5 Well-Posed Problems <br \/>6.1* Laplace\u2019s Equation<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/05\/06<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Well-posed problems for linear PDE systems (II).<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">1.5 Well-Posed Problems <br \/>6.3* Poisson\u2019s Formula<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2015\/05\/13<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Well-posed problems for linear PDE systems (III).<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.1* The Wave Equation<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/05\/20<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Nonlinear problems (I) - <br \/>The effect of a combination of nonlinearity and dispersion; <br \/>The effect of a combination of nonlinearity and dissipation; <br \/>The effect of a combination of nonlinearity, dispersion, and dissipation. <br \/>Shock waves, steady-state solutions, travelling wave solutions, soliton solutions, N-soliton solutions, and wavetrains.<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">14.1 Shock Waves <br \/>14.2 Solitary waves and Solitons <br \/>Supplement to lecture notes<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2015\/05\/2<\/span>7<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Nonlinear problems (II) - <br \/>kdV equation and the solitary solutions<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">14.1 Shock Waves <br \/>14.2 Solitary waves and Solitons <br \/>Supplement to lecture notes<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/06\/03<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Nonlinear Problems (III) - : Three famous universal nonlinear PDEs - kdV, s-G, and NLS equations. <br \/>Completely integrable systems s-G equation and the travelling wave solutions. <br \/>NLS equation and the solitary wave solutions.<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">14.2 Solitary waves and Solitons <br \/>Supplement to lecture notes<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2015\/06\/10<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Nonlinear Problems (IV) - Introduction of Riemann surfaces of genus N (1) for the underlying theory of solutions of universal nonlinear PDEs such as kdV, s-G, and NLS.<\/span><\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Supplement to lecture notes - Extension I of sec14.2 - the underlying theory of solutions of universal nonlinear PDEs (KdV, s-G, and NLS)<\/span><\/td><\/tr><tr><td style=\"text-align: center; padding: 5px;\"><span class=\"text\">2015\/06\/17<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Nonlinear Problems (V) - Introduction of Riemann surfaces of genus N (2) for the underlying theory of solutions of universal nonlinear PDEs such as kdV, s-G, and NLS.<\/span><\/td><td style=\"text-align: left; padding: 5px;\"><span class=\"text\">Supplement to lecture notes - Extension II of sec14-the underlying theory of solutions of universal nonlinear PDEs (KdV, s-G, and NLS)<\/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-d7723a8 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"d7723a8\" data-element_type=\"widget\" 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