{"id":29435,"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=29435"},"modified":"2022-09-14T15:55:26","modified_gmt":"2022-09-14T07:55:26","slug":"introduction-to-partial-differential-equations-department-of-applied-mathematics-prof-jong-eao-lee","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-partial-differential-equations-department-of-applied-mathematics-prof-jong-eao-lee","title":{"rendered":"Introduction to Partial Differential Equations | Department of Applied Mathematics Prof. Jong-Eao Lee"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"29435\" class=\"elementor elementor-29435\">\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 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href=\"https:\/\/ocw.nycu.edu.tw\/\">Homepage<\/a><\/span><\/span><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\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_12846\" 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\">Introduction to Partial Differential Equations<\/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  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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                                                            <span class=\"eael-tab-title  title-after-icon\">Course Homepage<\/span>                            \n                                                    <\/li>\n                                            <li id=\"video\" class=\"inactive eael-tab-item-trigger\" aria-selected=\"false\" data-tab=\"2\" role=\"tab\" tabindex=\"-1\" aria-controls=\"video-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-video\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336.2 64H47.8C21.4 64 0 85.4 0 111.8v288.4C0 426.6 21.4 448 47.8 448h288.4c26.4 0 47.8-21.4 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48-21.5 48-48V112c0-26.5-21.5-48-48-48zM96 424c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 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\">Course Syllabus<\/span>                            \n                                                    <\/li>\n                                            <li id=\"calendar\" class=\"inactive eael-tab-item-trigger\" 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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\">Course Calendar<\/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<\/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;\">Textbook\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;\">For perfect learning results, please buy textbooks!<\/span><\/p><p>\u00a0<\/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: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Department of Applied Mathematics Prof. Jong-Eao Lee <\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Course Credits<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03 Credits<\/span><\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Academic Year<\/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 Academic Year<\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Level<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Second year university student<\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Prior Knowledge<\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Differential Equations<\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Related Resources<\/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\">Course Video<\/a>\u00a0 \u00a0<a href=\"#syllabus\">Course Syllabus<\/a>\u00a0 \u00a0<a href=\"#calendar\">Course Calendar<\/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-67\" class=\"tablepress tablepress-id-67\">\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\">Week 01<\/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=29447&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\">Week 02<\/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=32811&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">Week 02<\/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=32817&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">Week 03<\/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=32826&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\">Week 04<\/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=32840&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">Week 05<\/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=32846&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">Week 06<\/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=32852&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">Week 07<\/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=32858&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">Week 08<\/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=32867\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\">Week 09<\/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=32879&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">Week 10<\/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=32884&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">Week 11<\/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=32890&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">Week 12<\/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=32896&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">Week 13<\/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=32902&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\">Week 14<\/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=32908&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\">Week 15<\/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=32914&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\">Week 16<\/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=32923&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\">Week 17<\/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=32929&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-67 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\" 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 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider .elementor-divider__element{margin:0 var(--divider-element-spacing);flex-shrink:0}.elementor-widget-divider .elementor-icon{font-size:var(--divider-icon-size)}.elementor-widget-divider .elementor-divider-separator{display:flex;margin:0;direction:ltr}.elementor-widget-divider--view-line_icon .elementor-divider-separator,.elementor-widget-divider--view-line_text 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href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-law\" class=\"elementor-item\" tabindex=\"-1\">School of Law<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\" tabindex=\"-1\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\" tabindex=\"-1\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\" tabindex=\"-1\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\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\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Introduction t&hellip;<\/p>\n","protected":false},"featured_media":29375,"parent":5277,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":{"footnotes":""},"categories":[242],"tags":[341,345,347,1411],"class_list":["post-29435","course_page","type-course_page","status-publish","format-standard","has-post-thumbnail","hentry","category-department-of-applied-mathematics-en","tag-label-all-course-en","tag-label-college-of-science-en","tag-label-am-en","tag-label-introduction-to-partial-differential-equations-103-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Introduction to Partial Differential Equations | 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