{"id":29352,"date":"2022-09-14T10:14:15","date_gmt":"2022-09-14T02:14:15","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=29352"},"modified":"2022-09-14T14:32:17","modified_gmt":"2022-09-14T06:32:17","slug":"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\/differential-equations-department-of-applied-mathematics-prof-jong-eao-lee","title":{"rendered":"Differential Equations | Department of Applied Mathematics Prof. Jong-Eao Lee\u00a0"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"29352\" class=\"elementor elementor-29352\">\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 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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_89356\" 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\">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        <div 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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 differential Equations \u2013 qualitative and quantative analysis.<br \/>First order differential equations.<br \/>Second order linear differential equations.<br \/>Higher order linear differential equations.<br \/>Second order nonlinear differential equations \u2013 pendulum motion.<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">Textbook\uff1a<\/span><\/p><p><span style=\"font-size: 16px;\">Differential Equations by P. Blanchard, R. L. Devaney, G. R. Hall, 4th edition Publisher: Cengage Learning<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\u00a0Credits<\/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;\">\u00a0Calculus<\/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-65\" class=\"tablepress tablepress-id-65\">\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\"><\/td><td class=\"column-2\">\u8ab2\u7a0b\u4ecb\u7d39<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=29368&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Introduction of ODE<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32473&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Big Picture for ODE<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32479&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1st order linear system<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32486&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1st order linear system: \u91cf\u7684\u5206\u6790<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32494&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2nd order linear equation with constant coefficients<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32499&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Practical Problem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32505&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Two more \u201cderivation\u201d of math models from:<br \/>\n--Predator-Prey problem<br \/>\n--Deposit and Withdraw problem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32511&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.2 ODE Big Picture<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32517&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.2 Mixed Problem<br \/>\n1.3 Slope Field<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32523&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.3 Slope Field<br \/>\n1.4 Numerical Technique<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32529&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.5 IVP\u89e3: \u5b58\u5728\u6027\u8207\u552f\u4e00\u6027<br \/>\n1.6 \u8cea\u5206\u6790, phase line(for autonomous system)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32535&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.7 Bifurcation and one supplement for 1.6(real problem)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32541&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Complete Chapter 1<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32549&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 2: 1st order system and 2nd order equation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32556&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.2 Geometry of the system(by vector field)<br \/>\n2.3 Damped harmonic oscillator<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32561&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.4 Special systems(solutions can be solved explicitly)<br \/>\n2.5 Euler\u2019s method for 1st order system<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32567&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.6 \u5b58\u5728\u8207\u552f\u4e00\u6027(for 1st order system)<br \/>\n2.7 (\u5047\u7684) 3D-system (\u6d41\u884c\u75c5\u50b3\u67d3\u554f\u984c)<br \/>\n2.8 (\u771f\u7684) 3D-system (\u6c23\u8c61\u9810\u5831\u7c21\u5316\u7cfb\u7d71: Lorenz equation)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32573&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.1 \u7dda\u6027\u7406\u8ad6<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32579&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.2 Straight-Line Solutions<br \/>\n3.3 Phase Portraits for Linear Systems with Real Eigenvalues<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32585&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.2 Straight-Line Solutions<br \/>\n3.3 Phase Portraits for Linear Systems with Real Eigenvalues<br \/>\n3.4 complex valued eigenvalues<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32600&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.5 Special cases of Linear systems<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32605&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">To complete 3.5<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32611&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.5 to complete<br \/>\n3.6 2nd order linear system and 2D linear system<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32618&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">To complete 3.6<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32623&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.7 Trace \u2013 Determinant Plane<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32629&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">To complete chapter 3<br \/>\n3.7 Part II: T-D plane<br \/>\n3.8 3D linear system<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32637&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Non-linear 2nd order ode:<br \/>\n--Pendulum motion<br \/>\n--Pendulum motion and spring motion<br \/>\n--Differences of phase portraits between linear and Nonlinear 2nd order equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32643&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Continue nonlinear 2nd order ode<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32649&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Special case for solving problems<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=32657&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-65 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 differential Equations \u2013 qualitative and quantative analysis.<\/p><p class=\"text\">First order differential equations.<\/p><p class=\"text\">Second order linear differential equations.<\/p><p class=\"text\">Higher order linear differential equations.<\/p><p class=\"text\">Second order nonlinear differential equations \u2013 pendulum motion.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u7ae0\u7bc0<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Introduction of ODE<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Introduction of ODE<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Big Picture for ODE<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.8 Linear Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">1st order linear system<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1.8 Linear Equations <br \/>1.9 Integrating Factors for Linear Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1st order linear system: \u91cf\u7684\u5206\u6790<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3.6 Second-Order Linear Equations <br \/>4.1 Forced Harmonic Oscillators <br \/>4.2 Sinusoidal Forcing<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">2nd order linear equation with constant coefficeints<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3.6 Second-Order Linear Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Practical Problem<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.1 Modeling via Differential Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Two more \u201cderivation\u201d of math models from: <br \/>Predator-Prey problem <br \/>Deposit and Withdraw problem<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">2.1 Modeling via Systems<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.2 ODE Big Picture<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.2 Analytic Technique: Separation of Variables<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">1.2 Mixed Problem <br \/>1.3 Slope Field<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1.2 Analytic Technique: Separation of Variables <br \/>1.3 Qualitative Technique: Slope Fields<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.3 Slope Field <br \/>1.4 Numerical Technique<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.3 Qualitative Technique: Slope Fields <br \/>1.4 Numerical Technique: Euler\u2019s Method<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">1.5 IVP\u89e3: \u5b58\u5728\u6027\u8207\u552f\u4e00\u6027 <br \/>1.6 \u8cea\u5206\u6790, phase line(for autonomous system)<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1.5 Existence and Uniqueness of Solutions <br \/>1.6 Equilibria and the Phase Line<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.7 Bifurcation and one supplement for 1.6(real problem)<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1.6 Equilibria and the Phase Line <br \/>1.7 Bifurcations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Complete Chapter 1<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1.1 Modeling via Differential Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Chapter 2: 1st order system and 2nd order equation<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.1 Modeling via Systems<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">2.2 Geometry of the system(by vector field) <br \/>2.3 Damped harmonic oscillator<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">2.2 The Geometry of Systems <br \/>2.3 The Damped Harmonic Oscillator<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.4 Special systems(solutions can be solved explicitly) <br \/>2.5 Euler\u2019s method for 1st order system<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2.4 Additional Analytic Methods for Special Systems <br \/>2.5 Euler\u2019s Method for Systems<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">2.6 \u5b58\u5728\u8207\u552f\u4e00\u6027(for 1st order system) <br \/>2.7 (\u5047\u7684) 3D-system (\u6d41\u884c\u75c5\u50b3\u67d3\u554f\u984c) <br \/>2.8 (\u771f\u7684) 3D-system (\u6c23\u8c61\u9810\u5831\u7c21\u5316\u7cfb\u7d71: Lorenz equation)<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">2.6 Existence and Uniqueness for Systems <br \/>2.7 The SIR Model of an Epidemic <br \/>2.8 The Lorenz Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3.1 \u7dda\u6027\u7406\u8ad6<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3.1 Properties of Linear Systems and the Linearity Principle<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">3.2 Straight-Line Solutions <br \/>3.3 Phase Portraits for Linear Systems with Real Eigenvalues<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3.2 Straight-Line Solutions <br \/>3.3 Phase Portraits for Linear Systems with Real Eigenvalues<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3.2 Straight-Line Solutions <br \/>3.3 Phase Portraits for Linear Systems with Real Eigenvalues <br \/>3.4 complex valued eigenvalues<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3.2 Straight-Line Solutions <br \/>3.3 Phase Portraits for Linear Systems with Real Eigenvalues <br \/>3.4 Complex Eigenvalues<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">3.5 Special cases of Linear systems<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3.5 Special Cases: Repeated and Zero Eigenvalues<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">To complete 3.5<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3.5 Special Cases: Repeated and Zero Eigenvalues<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">3.5 to complete <br \/>3.6 2nd order linear system and 2D linear system<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3.5 Special Cases: Repeated and Zero Eigenvalues<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">To complete 3.6<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3.6 Second-Order Linear Equations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">3.7 Trace \u2013 Determinant Plane<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">3.7 The Trace-Determinant Plane<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">To complete chapter 3 <br \/>3.7 Part II: T-D plane <br \/>3.8 3D linear system<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">3.7 The Trace-Determinant Plane 3.8 Linear Systems in Three Dimensions<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Non-linear 2nd order ode: <br \/>Pendulum motion <br \/>Pendulum motion and spring motion <br \/>Differences of phase portraits between linear and Nonlinear 2nd order equations<\/span><\/td><td style=\"padding: 5px;\">\u00a0<\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Continue nonlinear 2nd order ode<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\">\u00a0<\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Special case for solving problems<\/span><\/td><td style=\"padding: 5px;\">\u00a0<\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">Differential Equations by P. Blanchard, R. L. Devaney, G. R. Hall, 4th edition.<\/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;\" align=\"center\"><span style=\"font-weight: bold;\"><strong>\u6388\u8ab2\u4e3b\u984c<\/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;\"><p><span class=\"text\">2014\/09\/15<\/span><\/p><\/td><td style=\"text-align: left;\">Introduction of ODE<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>Introduction of ODE<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/09\/17<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">Big Picture for ODE<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>1.8 Linear Equations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/09\/22<\/span><\/td><td style=\"text-align: left;\">1st order linear system<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>1.8 Linear Equations <br \/>1.9 Integrating Factors for Linear Equations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">2014\/09\/24<\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">1st order linear system: \u91cf\u7684\u5206\u6790<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>3.6 Second-Order Linear Equations <br \/>4.1 Forced Harmonic Oscillators <br \/>4.2 Sinusoidal Forcing<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/09\/29<\/span><\/td><td style=\"text-align: left;\">2nd order linear equation with constant coefficeints<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>3.6 Second-Order Linear Equations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/10\/01<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">Practical Problem<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>1.1 Modeling via Differential Equations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/10\/06<\/span><\/td><td style=\"text-align: left;\">Two more \u201cderivation\u201d of math models from: <br \/>1. Predator-Prey problem <br \/>2. Deposit and Withdraw problem<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>2.1 Modeling via Systems<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/10\/08<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">1.2 ODE Big Picture<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>1.2 Analytic Technique: Separation of Variables<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/10\/13<\/span><\/td><td style=\"text-align: left;\">1.2 Mixed Problem<br \/>1.3 Slope Field<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>1.2 Analytic Technique: Separation of Variables <br \/>1.3 Qualitative Technique: Slope Fields<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#FFCC99\"><span class=\"text\">2014\/10\/15<\/span><\/td><td style=\"text-align: left; padding: 5px;\" colspan=\"2\" bgcolor=\"#FFCC99\">\u671f\u4e2d\u8003<\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/10\/20<\/span><\/td><td style=\"text-align: left;\">1.3 Slope Field <br \/>1.4 Numerical Technique<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>1.3 Qualitative Technique: Slope Fields <br \/>1.4 Numerical Technique: Euler\u2019s Method<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/10\/22<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">1.5 IVP\u89e3: \u5b58\u5728\u6027\u8207\u552f\u4e00\u6027 <br \/>1.6 \u8cea\u5206\u6790, phase line(for autonomous system)<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>1.5 Existence and Uniqueness of Solutions <br \/>1.6 Equilibria and the Phase Line<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/10\/27<\/span><\/td><td style=\"text-align: left;\">1.7 Bifurcation and one supplement for 1.6(real problem)<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>1.6 Equilibria and the Phase Line <br \/>1.7 Bifurcations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/10\/29<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">Complete Chapter 1<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>1.1 Modeling via Differential Equations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/11\/03<\/span><\/td><td style=\"text-align: left;\">Chapter 2: 1st order system and 2nd order equation<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>2.1 Modeling via Systems<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/11\/05<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">2.2 Geometry of the system(by vector field) <br \/>2.3 Damped harmonic oscillator<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>2.2 The Geometry of Systems <br \/>2.3 The Damped Harmonic Oscillator<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/11\/10<\/span><\/td><td style=\"text-align: left;\">2.4 Special systems(solutions can be solved explicitly) <br \/>2.5 Euler\u2019s method for 1st order system<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>2.4 Additional Analytic Methods for Special Systems <br \/>2.5 Euler\u2019s Method for Systems<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/11\/12<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">2.6 \u5b58\u5728\u8207\u552f\u4e00\u6027(for 1st order system) <br \/>2.7 (\u5047\u7684) 3D-system (\u6d41\u884c\u75c5\u50b3\u67d3\u554f\u984c) <br \/>2.8 (\u771f\u7684) 3D-system (\u6c23\u8c61\u9810\u5831\u7c21\u5316\u7cfb\u7d71: Lorenz equation)<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>2.6 Existence and Uniqueness for Systems <br \/>2.7 The SIR Model of an Epidemic <br \/>2.8 The Lorenz Equations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/11\/17<\/span><\/td><td style=\"text-align: left;\">3.1 \u7dda\u6027\u7406\u8ad6<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>3.1 Properties of Linear Systems and the Linearity Principle<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#FFCC99\"><span class=\"text\">2014\/11\/19<\/span><\/td><td style=\"text-align: left; padding: 5px;\" colspan=\"2\" bgcolor=\"#FFCC99\">\u671f\u4e2d\u8003<\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/11\/24<\/span><\/td><td style=\"text-align: left;\">3.2 Straight-Line Solutions <br \/>3.3 Phase Portraits for Linear Systems with Real Eigenvalues<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>3.2 Straight-Line Solutions <br \/>3.3 Phase Portraits for Linear Systems with Real Eigenvalues<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/11\/26<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">3.2 Straight-Line Solutions <br \/>3.3 Phase Portraits for Linear Systems with Real Eigenvalues <br \/>3.4 complex valued eigenvalues<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>3.2 Straight-Line Solutions <br \/>3.3 Phase Portraits for Linear Systems with Real Eigenvalues <br \/>3.4 Complex Eigenvalues<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/12\/01<\/span><\/td><td style=\"text-align: left;\">3.5 Special cases of Linear systems<\/td><td style=\"text-align: left;\"><ul><li>3.5 Special Cases: Repeated and Zero Eigenvalues<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#FFCC99\"><span class=\"text\">2014\/12\/03<\/span><\/td><td style=\"text-align: left; padding: 5px;\" colspan=\"2\" bgcolor=\"#FFCC99\">\u904b\u52d5\u6703<\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/12\/08<\/span><\/td><td style=\"text-align: left;\">To complete 3.5<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>3.5 Special Cases: Repeated and Zero Eigenvalues<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/12\/10<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">3.5 to complete <br \/>3.6 2nd order linear system and 2D linear system<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>3.5 Special Cases: Repeated and Zero Eigenvalues <br \/>3.6 Second-Order Linear Equations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/12\/15<\/span><\/td><td style=\"text-align: left;\">To complete 3.6<\/td><td style=\"text-align: left; padding: 5px;\"><ul><li>3.6 Second-Order Linear Equations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#FFCC99\"><span class=\"text\">2014\/12\/17<\/span><\/td><td style=\"text-align: left; padding: 5px;\" colspan=\"2\" bgcolor=\"#FFCC99\">\u671f\u4e2d\u8003<\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/12\/22<\/span><\/td><td style=\"text-align: left;\">3.7 Trace \u2013 Determinant Plane<\/td><td style=\"text-align: left;\"><ul><li>3.7 The Trace-Determinant Plane<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/12\/24<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">To complete chapter <br \/>3 3.7 Part II: T-D plane <br \/>3.8 3D linear system<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\"><ul><li>3.7 The Trace-Determinant Plane <br \/>3.8 Linear Systems in Three Dimensions<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/12\/29<\/span><\/td><td style=\"text-align: left;\">Non-linear 2nd order ode: <br \/>1. Pendulum motion <br \/>2. Pendulum motion and spring motion <br \/>3. Differences of phase portraits between linear and Nonlinear 2nd order equations<\/td><td style=\"text-align: left; padding: 5px;\">\u00a0<\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">2014\/12\/31<\/span><\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\">Continue nonlinear 2nd order ode<\/td><td style=\"text-align: left; padding: 5px;\" bgcolor=\"#f2f2ec\">\u00a0<\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">2014\/01\/05<\/span><\/td><td style=\"text-align: left;\">Special case for solving problems<\/td><td style=\"text-align: left;\">\u00a0<\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#FFCC99\"><span class=\"text\">2014\/01\/07<\/span><\/td><td style=\"text-align: left; padding: 5px;\" colspan=\"2\" bgcolor=\"#FFCC99\">\u671f\u672b\u8003<\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t                    <\/div>\n        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