{"id":26613,"date":"2022-09-10T19:51:44","date_gmt":"2022-09-10T11:51:44","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=26613"},"modified":"2026-03-09T15:39:38","modified_gmt":"2026-03-09T07:39:38","slug":"pde971_971217","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-science\/am\/%e5%81%8f%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e4%b8%80-partial-differential-equations-i-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e6%9e%97%e7%90%a6%e7%84%9c%e8%80%81%e5%b8%ab\/pde971_971217","title":{"rendered":"\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem, 3-6 Distribution Solutions"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"26613\" class=\"elementor elementor-26613\">\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 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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-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-5285c2d1 elementor-widget elementor-widget-penci-info-box\" data-id=\"5285c2d1\" 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_10141\" 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\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem, 3-6 Distribution Solutions\n<\/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-7aec5b11 elementor-widget elementor-widget-video\" data-id=\"7aec5b11\" data-element_type=\"widget\" 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penci-disSticky penci-structure-20 elementor-section elementor-inner-section elementor-element elementor-element-7c450277 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7c450277\" 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-inner-column elementor-element elementor-element-48607404\" data-id=\"48607404\" 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-652aa46c elementor-widget elementor-widget-penci-button\" data-id=\"652aa46c\" data-element_type=\"widget\" data-widget_type=\"penci-button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pcbtn-wrapper pcbtn-align-left\">\r\n\t\t\t<a class=\"pcbtn pcbtn-icon-left elementor-animation-grow\" href=\"\/?post_type=course_page&#038;p=24473\">\r\n\t\t\t\t<span class=\"pcbtn-wrapperin\">\r\n\t\t\t\t\t<span class=\"pcbtn-content\"><svg class=\"e-font-icon-svg e-fas-arrow-left\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M257.5 445.1l-22.2 22.2c-9.4 9.4-24.6 9.4-33.9 0L7 273c-9.4-9.4-9.4-24.6 0-33.9L201.4 44.7c9.4-9.4 24.6-9.4 33.9 0l22.2 22.2c9.5 9.5 9.3 25-.4 34.3L136.6 216H424c13.3 0 24 10.7 24 24v32c0 13.3-10.7 24-24 24H136.6l120.5 114.8c9.8 9.3 10 24.8.4 34.3z\"><\/path><\/svg>\u8fd4\u56de\u8ab2\u7a0b\u9996\u9801<\/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 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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-46\" class=\"tablepress tablepress-id-46\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">\u9031\u6b21<\/th><th class=\"column-2\">\u8ab2\u7a0b\u5167\u5bb9<\/th><th class=\"column-3\">\u8ab2\u7a0b\u5f71\u97f3<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-1 Introduction<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=24511\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-2 Examples<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26479\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-3 Analytic Solution and Approximation methods in a simple example<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26485\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-4  Quasilinear Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26491\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-5 The Cauchy Problem for the Quasilinear-linear Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26497\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-6 Examples<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26515\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-7 The general first-order equation for a function of two variables<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26521\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-8 The Cauchy Problem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26527\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 The Single First-Order Equation<br \/>\n1-9 Solutions generated as envelopes<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26533\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-1 Characteristics for Linear and Quasilinear Second-Order Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26539\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-2 Propagation of Singularity<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26545\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-3 The Linear Second-Order Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26551\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-4 The One-Dimensional Wave Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26557\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-5 System of First-Order Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26566\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables<br \/>\n2-6 A Quasi-linear System and Simple Waves<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26572\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-1 Natation of Laurent Schwartz<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26578\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-2 The Cauchy Problem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26584\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-3 Real Analytic Functions and the Cauchy-Kowalevski Theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26590\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-4 The Lagrange-Green Identity<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26601\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-5 The Uniqueness Theorem of Holmgren<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26607\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Characteristic Manifolds and Cauchy Problem<br \/>\n3-6 Distribution Solutions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26613\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-1 Greens Identity, Fundamental Solutions, and Poissons Equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26619\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-2 The Maximal Principle<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26625\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-3 The Dirichlet Problem, Greens Function, and Poisson Formula<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26639\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-4 Perrons method<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26645\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u56db\u7ae0 The Laplace Equation<br \/>\n4-5 Solution of the Dirichlet Problem by Hilbert-Space Methods<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=26651\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-46 from cache --><\/div>\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-3 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element 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