{"id":32852,"date":"2022-09-24T19:34:15","date_gmt":"2022-09-24T11:34:15","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=32852"},"modified":"2026-06-08T14:47:38","modified_gmt":"2026-06-08T06:47:38","slug":"classification-of-3-types-of-second-order-linear-pdes-ii-initial-value-problem-for-a-whole-line-linear-heat-equation-solved-by-the-fundamental-solution","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\/classification-of-3-types-of-second-order-linear-pdes-ii-initial-value-problem-for-a-whole-line-linear-heat-equation-solved-by-the-fundamental-solution","title":{"rendered":"Classification of 3 types of second order linear PDEs (II). Initial value problem for a whole-line linear heat equation solved by the Fundamental solution."},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"32852\" class=\"elementor elementor-32852\">\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-16700d17 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"16700d17\" 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-1832f798\" data-id=\"1832f798\" 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-4a3731c elementor-widget elementor-widget-breadcrumbs\" data-id=\"4a3731c\" data-element_type=\"widget\" data-widget_type=\"breadcrumbs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<link rel=\"stylesheet\" href=\"https:\/\/ocw.nycu.edu.tw\/wp-content\/plugins\/elementor-pro\/assets\/css\/widget-theme-elements.min.css\"><p id=\"breadcrumbs\"><span><span><a 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-6ad968e6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6ad968e6\" 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-52987d63\" data-id=\"52987d63\" 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-e5808cb elementor-widget elementor-widget-heading\" data-id=\"e5808cb\" data-element_type=\"widget\" data-widget_type=\"heading.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-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Classification of 3 types of second order linear PDEs (II). Initial value problem for a whole-line linear heat equation solved by the Fundamental solution.\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7aec5b11 elementor-widget elementor-widget-video\" data-id=\"7aec5b11\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/hsmVWhqdHRM&quot;,&quot;modestbranding&quot;:&quot;yes&quot;,&quot;lazy_load&quot;:&quot;yes&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.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-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper 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to Course Homepage<\/span>\r\n\t\t\t\t\t\t\t\t\t<\/span>\r\n\t\t\t<\/a>\r\n\t\t<\/div>\r\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<div class=\"penci-ercol-50 penci-ercol-order-2 penci-sticky-ct    elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-fc8fc3b\" data-id=\"fc8fc3b\" 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<div class=\"elementor-element elementor-element-546b36ef elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"546b36ef\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 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100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da19150 elementor-widget elementor-widget-shortcode\" data-id=\"da19150\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">\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 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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 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