{"id":129568,"date":"2024-10-21T10:21:04","date_gmt":"2024-10-21T02:21:04","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=129568"},"modified":"2025-07-09T14:47:58","modified_gmt":"2025-07-09T06:47:58","slug":"calculus-a-ii-academic-109-en","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/calculus-a-ii-academic-109-en","title":{"rendered":"Calculus I (B) Academic Year 109 | Department of Applied Mathematics Prof. Cheng-Fang Su"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"129568\" class=\"elementor elementor-129568\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-90a0113 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"90a0113\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-100 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-78bf394\" data-id=\"78bf394\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-0025485 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0025485\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-0446ed9\" data-id=\"0446ed9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f5840a elementor-widget elementor-widget-penci-info-box\" data-id=\"2f5840a\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_3609\" 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\">Calculus I (B) -  Academic Year 109<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6381f4 elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"c6381f4\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        <div id=\"eael-advance-tabs-c6381f4\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"c6381f4\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                                            <li id=\"home\" class=\"active-default eael-tab-item-trigger\" aria-selected=\"true\" data-tab=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"home-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-home\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M280.37 148.26L96 300.11V464a16 16 0 0 0 16 16l112.06-.29a16 16 0 0 0 15.92-16V368a16 16 0 0 1 16-16h64a16 16 0 0 1 16 16v95.64a16 16 0 0 0 16 16.05L464 480a16 16 0 0 0 16-16V300L295.67 148.26a12.19 12.19 0 0 0-15.3 0zM571.6 251.47L488 182.56V44.05a12 12 0 0 0-12-12h-56a12 12 0 0 0-12 12v72.61L318.47 43a48 48 0 0 0-61 0L4.34 251.47a12 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 47.8-47.8V111.8c0-26.4-21.4-47.8-47.8-47.8zm189.4 37.7L416 177.3v157.4l109.6 75.5c21.2 14.6 50.4-.3 50.4-25.8V127.5c0-25.4-29.1-40.4-50.4-25.8z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">Course Video<\/span>                            \n                                                    <\/li>\n                                            <li id=\"syllabus\" class=\"inactive eael-tab-item-trigger\" aria-selected=\"false\" data-tab=\"3\" role=\"tab\" tabindex=\"-1\" aria-controls=\"syllabus-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-clipboard-list\" viewBox=\"0 0 384 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336 64h-80c0-35.3-28.7-64-64-64s-64 28.7-64 64H48C21.5 64 0 85.5 0 112v352c0 26.5 21.5 48 48 48h288c26.5 0 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=\"notes\" class=\"inactive eael-tab-item-trigger\" aria-selected=\"false\" data-tab=\"4\" role=\"tab\" tabindex=\"-1\" aria-controls=\"notes-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg e-fas-clipboard-list\" viewBox=\"0 0 384 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336 64h-80c0-35.3-28.7-64-64-64s-64 28.7-64 64H48C21.5 64 0 85.5 0 112v352c0 26.5 21.5 48 48 48h288c26.5 0 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\">Learning Notes<\/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\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><br \/>.\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;\">This course is provided by the <a href=\"https:\/\/www.math.nycu.edu.tw\/\" target=\"_blank\" rel=\"noopener\">\u00a0NYCU Department of Applied Mathematics .<\/a><\/p><p>Calculus is a fundamental tool in various fields such as physics, biology, statistics, astronomy, economics, computer science, and financial engineering. It also serves as a prerequisite for many courses, such as engineering mathematics, differential equations, statistics, and financial mathematics.<\/p><p class=\"text\">Calculus I (B) builds upon the knowledge from Calculus I (A), covering topics such as the convergence and applications of sequences and series, limits and continuity of multivariable functions, partial derivatives, directional derivatives, gradients, and differentiability of functions. The course will also introduce the computation and applications of multiple integrals and conclude with the basics of vector calculus. These topics are crucial for analyzing practical problems in fields such as electromagnetism, fluid mechanics, and economics. This course aims to help students establish a solid understanding of the fundamental theories and computational techniques of multivariable calculus, which will be useful for subsequent courses and research.<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">Textbook\uff1a<\/span><\/p><p><span style=\"font-size: 16px;\">Stewart, James. <em>Calculus: Early Transcendentals<\/em>., 8th ed. Cengage Learning, 2015.<\/span><\/p><p><span style=\"color: #ff00ff;\">For perfect learning results, please buy textbooks!<\/span><\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Instructor(s)<\/span><\/span><\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Department of Applied Mathematics Prof. Cheng-Fang Su<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Course Credits<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a04 Credits<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Academic Year<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0109 Academic Year<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Level<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0College Students<br \/><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Prior Knowledge<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0High school mathematics<\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">Related Resources<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><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<a href=\"#notes\">Learning Notes<\/a><\/span><\/span><\/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-594\" class=\"tablepress tablepress-id-594\">\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\">1<\/td><td class=\"column-2\">Chapter 8 Sequences, Series, and Power Series<br \/>\nIntroduction<br \/>\n8.1 Sequences<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129619\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\">2<\/td><td class=\"column-2\">8.1 Sequences<br \/>\n8.2 Series<br \/>\n8.3 The Integral Test<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129788\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">3<\/td><td class=\"column-2\">8.1-8.3\u7684\u88dc\u5145\u4f8b\u984c (Other Examples for 8.1-8.3)<br \/>\n8.4 Comparison Tests<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129793\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">4<\/td><td class=\"column-2\">\u6b63\u9805\u7d1a\u6578\u6582\u6563\u6027\u7684\u8907\u7fd2 (Review of the Test for Convergence of Series with Non-negative Terms)<br \/>\n8.5 The Ratio and Root Tests<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129798\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\">5<\/td><td class=\"column-2\">8.6 Alternating Series and Absolute Convergence<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129803\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">6<\/td><td class=\"column-2\">8.7 Power Series<br \/>\n8.8 Representation of Functions as Power Series(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129811\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">7<\/td><td class=\"column-2\">8.8 Representation of Functions as Power Series(2\/2)<br \/>\n8.9 Taylor Series and Maclaurin Series(1\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129816\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">8<\/td><td class=\"column-2\">8.9 Taylor Series and Maclaurin Series(2\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129821\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">9<\/td><td class=\"column-2\">8.9 Taylor Series and Maclaurin Series(3\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129826\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\">10<\/td><td class=\"column-2\">Rearrangement of Series and Binomial Series<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129831\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">11<\/td><td class=\"column-2\">Chapter 9 Vector and the Geometry of Space<br \/>\n9.1 Vectors in the Plane<br \/>\n9.2 Vectors in Space<br \/>\n9.3 The Dot Product of Two Vectors in Space<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129836\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">12<\/td><td class=\"column-2\">Chapter 10 Vector Functions<br \/>\n10.1 Vector Functions and Space Curves(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129841\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">13<\/td><td class=\"column-2\">10.1 Vector Functions and Space Curves(2\/2)<br \/>\n10.2 Differentiation and Integration of Vector Function(1\/2)<br \/>\n<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129846\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">14<\/td><td class=\"column-2\">10.2 Differentiation and Integration of Vector Function(2\/2)<br \/>\n10.3 Arc Length and Curvature(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129851\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\">15<\/td><td class=\"column-2\">10.3 Arc Length and Curvature(2\/2)<br \/>\nChapter 11 Partial Derivatives<br \/>\n11.1 Functions of Several Variables<br \/>\n11.2 Limits and Continuity(1\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129856\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\">16<\/td><td class=\"column-2\">11.2 Limits and Continuity(2\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129861\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\">17<\/td><td class=\"column-2\">11.2 Limits and Continuity(3\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129866\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\">18<\/td><td class=\"column-2\">11.3 Partial Derivatives<br \/>\n11.4 Tangent Plane and Linear Approximation(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129871\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\">19<\/td><td class=\"column-2\">11.4 Tangent Plane and Linear Approximation(2\/2)<br \/>\n11.5 The Chain Rule(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129876\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\">20<\/td><td class=\"column-2\">11.5 The Chain Rule(2\/2)<br \/>\n11.6 Directional Derivatives and the Gradient Vector(1\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129881\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\">21<\/td><td class=\"column-2\">11.6 Directional Derivatives and the Gradient Vector(2\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129887\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\">22<\/td><td class=\"column-2\">11.6 Directional Derivatives and the Gradient Vector(3\/3)<br \/>\n11.7 Maximum and Minimum Values(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129892\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\">23<\/td><td class=\"column-2\">11.7 Maximum and Minimum Values(2\/2)<br \/>\n11.8 Lagrange Multiplier Method<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129897\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\">24<\/td><td class=\"column-2\">Chapter 12 Multiple Integrals<br \/>\n12.1 Iterated Integrals(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129902\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\">25<\/td><td class=\"column-2\">12.1 Iterated Integrals(2\/2)<br \/>\n12.2 Double Integrals(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129907\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\">26<\/td><td class=\"column-2\">12.2 Double Integrals(2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129912\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\">27<\/td><td class=\"column-2\">12.3 Double Integrals in Polar Coordinates<br \/>\n12.4 Surface Area<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129917\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\">28<\/td><td class=\"column-2\">12.5 Triple Integrals(1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129922\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\">29<\/td><td class=\"column-2\">12.5 Triple Integrals(2\/2)<br \/>\n12.6 Triple Integrals in Cylindrical Coordinates<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129927\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\">30<\/td><td class=\"column-2\">12.7 Triple Integrals in Spherical Coordinates<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129932\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\">31<\/td><td class=\"column-2\">12.8 Change of Variables in Multiple Integrals<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=129937\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u00a0<\/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>Course Objectives<br \/><\/strong><\/p><p class=\"text\">Calculus is a fundamental tool in various fields such as physics, biology, statistics, astronomy, economics, computer science, and financial engineering. It also serves as a prerequisite for many courses, such as engineering mathematics, differential equations, statistics, and financial mathematics.<br \/>Calculus I (B) builds upon the knowledge from Calculus I (A), covering topics such as the convergence and applications of sequences and series, limits and continuity of multivariable functions, partial derivatives, directional derivatives, gradients, and differentiability of functions. The course will also introduce the computation and applications of multiple integrals and conclude with the basics of vector calculus. These topics are crucial for analyzing practical problems in fields such as electromagnetism, fluid mechanics, and economics. This course aims to help students establish a solid understanding of the fundamental theories and computational techniques of multivariable calculus, which will be useful for subsequent courses and research.<\/p><p class=\"title\"><strong>Course Chapter<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><b>Chapter<\/b><\/td><td bgcolor=\"#e4d8b0\"><b>Content<\/b><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Chapter 8 Sequences, Series, and Power Series<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">8.1 Sequences<br \/>8.2 Series<br \/>8.3 The Integral Test)<br \/>8.4 Comparison Tests<br \/>8.5 The Ratio and Root Tests<br \/>8.6 Alternating Series and Absolute Convergence<br \/>8.7 Power Series<br \/>8.8 Representation of Functions as Power Series8.9 Taylor Series and Maclaurin Series<br \/>Rearrangement of Series and Binomial Series<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Chapter 9 Vector and the Geometry of Space<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">9.1 Vectors in the Plane<br \/>9.2 Vectors in Space<br \/>9.3 The Dot Product of Two Vectors in Space<br \/><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Chapter 10 Vector Functions<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">10.1 Vector Functions and Space Curves<br \/>10.2 Differentiation and Integration of Vector Function<br \/>10.3 Arc Length and Curvature<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Chapter 11 Partial Derivatives<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">11.1 Functions of Several Variables<br \/>11.2 Limits and Continuity<br \/>11.3 Partial Derivatives<br \/>11.4 Tangent Plane and Linear Approximation<br \/>11.5 The Chain Rule<br \/>11.6 Directional Derivatives and the Gradient Vector<br \/>11.7 Maximum and Minimum Values<br \/>11.8 Lagrange Multiplier Method<br \/><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Chapter 12 Multiple Integrals<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">12.1 Iterated Integrals<br \/>12.2 Double Integrals<br \/>12.3 Double Integrals in Polar Coordinates<br \/>12.4 Surface Area<br \/>12.5 Triple Integrals<br \/>12.6 Triple Integrals in Cylindrical Coordinates<br \/>12.7 Triple Integrals in Spherical Coordinates<br \/>12.8 Change of Variables in Multiple Integrals<br \/><\/span><\/td><\/tr><\/tbody><\/table><p class=\"title\"><strong>Textbooks<\/strong><\/p><p class=\"text\">Stewart,\u00a0James.\u00a0<em>Calculus: Early Transcendentals<\/em>., 8th ed. Cengage Learning, 2015.<\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"notes-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"notes-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><strong class=\"title\">\u5b78\u7fd2\u7b46\u8a18 Learning Notes<\/strong><\/p><table border=\"1\" width=\"98% cellspacing=\"><tbody><tr class=\"stitle\"><td colspan=\"2\" bgcolor=\"#e4d8b0\"><strong> \u5b78\u7fd2\u7b46\u8a18-\u7531\u5149\u96fb\u5de5\u7a0b\u5b78\u7cfb\u9673\u555f\u99bc\u540c\u5b78\u63d0\u4f9b<\/strong><\/td><\/tr><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong>Chapter<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong>Download Link<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">1. \u55ae\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u6975\u9650\u8207\u9023\u7e8c<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes01.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr bgcolor=\"#EEEEEE\"><td style=\"padding: 5px;\"><span class=\"text\">2. \u55ae\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u5c0e\u6578\uff08\u6982\u5ff5\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes01.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">3. \u55ae\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u5c0e\u6578\uff08\u61c9\u7528\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes03.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr bgcolor=\"#EEEEEE\"><td style=\"padding: 5px;\"><span class=\"text\">4.\u00a0\u55ae\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u7a4d\u5206\uff08\u6982\u5ff5\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes04.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">5. \u55ae\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u7a4d\u5206\uff08\u6280\u5de7\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes05.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr bgcolor=\"#EEEEEE\"><td style=\"padding: 5px;\"><span class=\"text\">6. \u55ae\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u7455\u7a4d\u5206<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes06.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">7. \u55ae\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u7a4d\u5206\uff08\u61c9\u7528\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes07.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">8. \u53c3\u6578\u65b9\u7a0b\u5f0f<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes08.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr bgcolor=\"#EEEEEE\"><td style=\"padding: 5px;\"><span class=\"text\">9. \u6578\u5217\u8207\u7d1a\u6578<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes09.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">10. \u55ae\u8b8a\u6578\u5411\u91cf\u51fd\u6578\uff08\u6982\u5ff5\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes10.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr bgcolor=\"#EEEEEE\"><td style=\"padding: 5px;\"><span class=\"text\">11. \u55ae\u8b8a\u6578\u5411\u91cf\u51fd\u6578\uff08\u61c9\u7528\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes11.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">12. \u591a\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u6975\u9650\u8207\u9023\u7e8c<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes12.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr bgcolor=\"#EEEEEE\"><td style=\"padding: 5px;\"><span class=\"text\">13. \u591a\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u504f\u5c0e\u6578\uff08\u6982\u5ff5\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes13.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">14. \u591a\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u504f\u5c0e\u6578\uff08\u61c9\u7528\u7bc7\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes14.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr bgcolor=\"#EEEEEE\"><td style=\"padding: 5px;\"><span class=\"text\">15. \u591a\u8b8a\u6578\u7d14\u91cf\u51fd\u6578\u2014\u91cd\u7a4d\u5206<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes15.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">16. \u7b46\u8a18\uff08\u5168\uff09<\/span><\/td><td style=\"padding: 5px; text-align: center;\"><span class=\"text\"><a href=\"https:\/\/video.ocw.nycu.edu.tw\/pub\/ca091\/ca091ca092_studynotes16.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a><\/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 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class=\"elementor-item\" tabindex=\"-1\">College of Hakka Affair Culture<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118070\"><a 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>Calculus I (B)&hellip;<\/p>\n","protected":false},"featured_media":129532,"parent":5277,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":{"footnotes":""},"categories":[242],"tags":[341,345,347,10159,10734],"class_list":["post-129568","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-pre-university-courses-en","tag-label-calculus-i-b-109-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Calculus I (B) Academic Year 109 | Department of Applied Mathematics Prof. Cheng-Fang Su - NYCU OCW<\/title>\n<meta name=\"description\" content=\"Calculus I (B) - Academic Year 109 Course Homepage Course Video Course Syllabus Learning Notes This course is provided by the \u00a0NYCU 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