{"id":40909,"date":"2022-10-13T19:48:28","date_gmt":"2022-10-13T11:48:28","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=40909"},"modified":"2026-06-29T11:59:29","modified_gmt":"2026-06-29T03:59:29","slug":"iii-line-integrals-and-multiple-integrals-iii-3-line-integral-iii-4-applied-to-physical-chemistry-i-iii-5-double-integral-iii-6-jacobi-determinant","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-chemistry\/applied-mathematics-department-of-applied-chemistry-prof-chao-yuan-zhu\/iii-line-integrals-and-multiple-integrals-iii-3-line-integral-iii-4-applied-to-physical-chemistry-i-iii-5-double-integral-iii-6-jacobi-determinant","title":{"rendered":"III. Line integrals and multiple integrals, III-3. Line integral, III-4. Applied to Physical Chemistry I, III-5. Double integral, III-6. Jacobi determinant"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"40909\" class=\"elementor elementor-40909\">\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\">III. Line integrals and multiple integrals, III-3. Line integral, III-4. Applied to Physical Chemistry I, III-5. Double integral, III-6. Jacobi determinant\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\\\/vxOXIxOog7I&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 video{height:100%;width:100%;display:flex;border:none;background-color:#000}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-wrapper{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .elementor-open-inline .elementor-custom-embed-image-overlay{position:absolute;top:0;left:0;width:100%;height:100%;background-size:cover;background-position:50%}.elementor-widget-video .elementor-custom-embed-image-overlay{cursor:pointer;text-align:center}.elementor-widget-video .elementor-custom-embed-image-overlay:hover .elementor-custom-embed-play i{opacity:1}.elementor-widget-video .elementor-custom-embed-image-overlay img{display:block;width:100%}.elementor-widget-video .e-hosted-video .elementor-video{-o-object-fit:cover;object-fit:cover}.e-con-inner>.elementor-widget-video,.e-con>.elementor-widget-video{width:var(--container-widget-width);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"penci-section 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=37770\">\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>Back 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 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider .elementor-divider__element{margin:0 var(--divider-element-spacing);flex-shrink:0}.elementor-widget-divider .elementor-icon{font-size:var(--divider-icon-size)}.elementor-widget-divider .elementor-divider-separator{display:flex;margin:0;direction:ltr}.elementor-widget-divider--view-line_icon .elementor-divider-separator,.elementor-widget-divider--view-line_text .elementor-divider-separator{align-items:center}.elementor-widget-divider--view-line_icon .elementor-divider-separator:after,.elementor-widget-divider--view-line_icon .elementor-divider-separator:before,.elementor-widget-divider--view-line_text .elementor-divider-separator:after,.elementor-widget-divider--view-line_text .elementor-divider-separator:before{display:block;content:\"\";border-bottom:0;flex-grow:1;border-top:var(--divider-border-width) var(--divider-border-style) var(--divider-color)}.elementor-widget-divider--element-align-left .elementor-divider .elementor-divider-separator>.elementor-divider__svg:first-of-type{flex-grow:0;flex-shrink:100}.elementor-widget-divider--element-align-left .elementor-divider-separator:before{content:none}.elementor-widget-divider--element-align-left .elementor-divider__element{margin-left:0}.elementor-widget-divider--element-align-right .elementor-divider .elementor-divider-separator>.elementor-divider__svg:last-of-type{flex-grow:0;flex-shrink:100}.elementor-widget-divider--element-align-right .elementor-divider-separator:after{content:none}.elementor-widget-divider--element-align-right .elementor-divider__element{margin-right:0}.elementor-widget-divider:not(.elementor-widget-divider--view-line_text):not(.elementor-widget-divider--view-line_icon) .elementor-divider-separator{border-top:var(--divider-border-width) var(--divider-border-style) var(--divider-color)}.elementor-widget-divider--separator-type-pattern{--divider-border-style:none}.elementor-widget-divider--separator-type-pattern.elementor-widget-divider--view-line .elementor-divider-separator,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:after,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:before,.elementor-widget-divider--separator-type-pattern:not([class*=elementor-widget-divider--view]) .elementor-divider-separator{width:100%;min-height:var(--divider-pattern-height);-webkit-mask-size:var(--divider-pattern-size) 100%;mask-size:var(--divider-pattern-size) 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-95\" class=\"tablepress tablepress-id-95\">\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\">I. Review of differentiation and integration<br \/>\nI-1. Introduction<br \/>\nI-2. Review of differential calculus<br \/>\nI-3. Review of integral calculus<br \/>\nI-4. Graph<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38092\">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\">II. Calculus of several variables, partial differentiation<br \/>\nII-1. Partial derivatives<br \/>\nII-2. Total differential<br \/>\nII-3. Application to physical chemistry I <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40888\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">Week 03<\/td><td class=\"column-2\">II. Calculus of several variables, partial differentiation<br \/>\nII-4. Cycle rule<br \/>\nII-5. Application of derivatives<br \/>\nII-6. van Der Waals equation of state <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40894\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">Week 04<\/td><td class=\"column-2\">II. Calculus of several variables, partial differentiation<br \/>\nII-7. Constrained maxima and minima<br \/>\nII-8. Stirling\u2019s formula<br \/>\nII-9.Application to physical chemistry III<br \/>\nIII. Line integrals and multiple integrals<br \/>\nIII-1. Introduction <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40900\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\">Week 05<\/td><td class=\"column-2\">III. Line integrals and multiple integrals<br \/>\nIII-3. Line integral<br \/>\nIII-4. Applied to Physical Chemistry I<br \/>\nIII-5. Double integral<br \/>\nIII-6. Jacobi determinant <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40909\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">Week 06<\/td><td class=\"column-2\">IV. Infinite series<br \/>\nIV-1. Talyor series<br \/>\nIV-2. Convergence and its region<br \/>\nIV-3. Applied to Physical Chemistry II <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40915\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">Week 07<\/td><td class=\"column-2\">IV. Infinite series<br \/>\nIV-4. Fourier series<br \/>\nIV-5. Particle in one-dimensional box (PC II)<br \/>\nIV-6. Kronecker delta function<br \/>\nIV-7. Fourier transforms <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40921\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">Week 08<\/td><td class=\"column-2\">\u4f5c\u696d\u8a0e\u8ad6<br \/>\nFourier series<br \/>\nFourier transforms <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40927\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">Week 10<\/td><td class=\"column-2\">V. Ordinary differential equations (1\/4)<br \/>\nV-1. Introduction<br \/>\nV-2. The first-order differential equations<br \/>\nV-3. The second-order differential equations <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40933\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\">Week 11<\/td><td class=\"column-2\">V. Ordinary differential equations (2\/4)<br \/>\nV-4. Differential equations with total differential <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40939\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">Week 12<\/td><td class=\"column-2\">V. Ordinary differential equations (3\/4)<br \/>\nV-5. Special functions for the second-order DE\u3001Quantum harmonic oscillator\u3001Quantum hydrogen atom<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40945\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">Week 13<\/td><td class=\"column-2\">V. Ordinary differential equations (4\/4)<br \/>\nV-5. Special functions for the second-order DE\u3001Quantum harmonic oscillator\u3001Quantum hydrogen atom <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40951\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">Week 14<\/td><td class=\"column-2\">VI. Partial differential equations<br \/>\nVI-1. Introduction<br \/>\nVI-2. The classical wave<br \/>\nVII. Determinants and matrices (1\/4)<br \/>\nVII-1 Introduction <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40957\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">Week 15<\/td><td class=\"column-2\">VII. Determinants and matrices (2\/4)<br \/>\nVII-2. Determinant algebra<br \/>\nVII-3. Properties of determinant<br \/>\nVII-4. Matrix algebra<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40963\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\">Week 16<\/td><td class=\"column-2\">VII. Determinants and matrices (3\/4)<br \/>\nVII-5. Singular matrix<br \/>\nVII-6. Characteristic equation of a matrix<br \/>\nVII-7. Symmetry matrix<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=40969\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\">Week 17<\/td><td class=\"column-2\">VII. Determinants and matrices (4\/4)<br \/>\nVII-8. 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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 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 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Line inte&hellip;<\/p>\n","protected":false},"featured_media":0,"parent":37770,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","format":"standard","meta":{"footnotes":""},"categories":[1730],"tags":[],"class_list":["post-40909","course_page","type-course_page","status-publish","format-standard","hentry","category-applied-mathematics-101-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>III. Line integrals and multiple integrals, III-3. Line integral, III-4. Applied to Physical Chemistry I, III-5. Double integral, III-6. Jacobi determinant - NYCU OCW<\/title>\n<meta name=\"description\" content=\"III. Line integrals and multiple integrals, III-3. Line integral, III-4. Applied to Physical Chemistry I, III-5. Double integral, III-6. 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