{"id":491,"date":"2023-07-17T12:53:32","date_gmt":"2023-07-17T17:53:32","guid":{"rendered":"https:\/\/ceid1.wpenginepowered.com\/HYPAD\/?page_id=491"},"modified":"2024-04-12T14:18:38","modified_gmt":"2024-04-12T19:18:38","slug":"lecture-notes","status":"publish","type":"page","link":"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/","title":{"rendered":"Lecture Notes"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"491\" class=\"elementor elementor-491\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7ab1e13 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7ab1e13\" data-element_type=\"section\" data-e-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=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a89101d\" data-id=\"a89101d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-97362c8 elementor-widget elementor-widget-heading\" data-id=\"97362c8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Hypercomplex Automatic Differentiation (HYPAD) Lecture Notes<\/h2>\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b84140f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b84140f\" data-element_type=\"section\" data-e-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=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-496e8c1\" data-id=\"496e8c1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fb44e9a elementor-widget elementor-widget-text-editor\" data-id=\"fb44e9a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The following tabs contains lecture notes on hypercomplex automatic differentiation.<\/p>\t\t\t\t\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<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4254f70 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4254f70\" data-element_type=\"section\" data-e-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=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-feb9248\" data-id=\"feb9248\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-63513a0 elementor-widget elementor-widget-toggle\" data-id=\"63513a0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1041\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1041\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Complex Step Lecture Notes<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1041\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1041\"><ol><li><em><span style=\"font-size: 14pt\"><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/1-hypad-course-complex-step-derivation-1.pdf\" target=\"_blank\" rel=\"noopener\">Derivation<\/a><\/span><\/em><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/2-HYPAD-Course-complex-step-Closed-Form.pdf\" target=\"_blank\" rel=\"noopener\">Closed Form<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/3-hypad-course-complex-step-special-functions.pdf\" target=\"_blank\" rel=\"noopener\">Special Functions<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/4-hypad-course-complex-step-step-size-study.pdf\" target=\"_blank\" rel=\"noopener\">Step Size Study<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/5-hypad-course-complex-step-numerical-integration.pdf\" target=\"_blank\" rel=\"noopener\">Numerical Integration<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/6-hypad-course-complex-step-newton-rhapson.pdf\">Newton Rhapson<\/a><\/em><\/span><\/li><li><em><span style=\"font-size: 14pt\"><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/7-hypad-course-complex-step-ode-solver.pdf\" target=\"_blank\" rel=\"noopener\">ODE Solver<\/a><\/span><\/em><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/8-hypad-course-complex-step-c-r-format.pdf\" target=\"_blank\" rel=\"noopener\">CR Format<\/a><\/em><\/span><\/li><li><em><span style=\"font-size: 14pt\"><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/9-hypad-course-complex-step-2nd-order.pdf\" target=\"_blank\" rel=\"noopener\">2nd Order<\/a><\/span><\/em><\/li><\/ol><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1042\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-1042\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Dual Lecture Notes<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1042\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-1042\"><ol><li><em><span style=\"font-size: 14pt\"><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/1-HYPAD-Course-duals-Derivation-1.pdf\" target=\"_blank\" rel=\"noopener\">Derivation<\/a><\/span><\/em><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/2-HYPAD-Course-duals-ClosedForm.pdf\" target=\"_blank\" rel=\"noopener\">Closed Form<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/3-HYPAD-Course-duals-StepSizeStudy.pdf\" target=\"_blank\" rel=\"noopener\">Step Size Study<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/4-HYPAD-Course-duals-NumericalIntegration.pdf\" target=\"_blank\" rel=\"noopener\">Numerical Integration<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/5-HYPAD-Course-duals-NewtonRhapson.pdf\" target=\"_blank\" rel=\"noopener\">Newton Rhapson<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/6-HYPAD-Course-duals-ODESolver.pdf\" target=\"_blank\" rel=\"noopener\">ODE Solver<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/7-HYPAD-Course-duals-CRFormat.pdf\" target=\"_blank\" rel=\"noopener\">CR Format<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/8-HYPAD-Course-duals-2ndOrder.pdf\" target=\"_blank\" rel=\"noopener\">2nd Order<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/9-HYPAD-Course-duals-ComplexFunctions.pdf\" target=\"_blank\" rel=\"noopener\">Complex Functions<\/a><\/em><\/span><\/li><\/ol><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1043\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-1043\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Bidual Lecture Notes<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1043\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-1043\"><ol><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/1-HYPAD-Course-biduals-Derivation.pdf\" target=\"_blank\" rel=\"noopener\">Derivation<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/2-HYPAD-Course-biduals-Functions.pdf\" target=\"_blank\" rel=\"noopener\">Functions<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/3-HYPAD-Course-biduals-ClosedForm-2.pdf\" target=\"_blank\" rel=\"noopener\">Closed Form<\/a><\/em><\/span><\/li><li><span style=\"font-size: 14pt\"><em><a href=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/03\/8-HYPAD-Course-biduals-CRFormat-2.pdf\" target=\"_blank\" rel=\"noopener\">CR Format<\/a><\/em><\/span><\/li><\/ol><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\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<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Hypercomplex Automatic Differentiation (HYPAD) Lecture Notes The following tabs contains lecture notes on hypercomplex automatic differentiation. Complex Step Lecture Notes Derivation Closed Form Special Functions Step Size Study Numerical Integration Newton Rhapson ODE Solver CR Format 2nd Order Dual Lecture Notes Derivation Closed Form Step Size Study Numerical Integration Newton Rhapson ODE Solver CR Format [&hellip;]<\/p>\n","protected":false},"author":248,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-491","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Lecture Notes - HYPercomplex Automatic Differentiation<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lecture Notes - HYPercomplex Automatic Differentiation\" \/>\n<meta property=\"og:description\" content=\"Hypercomplex Automatic Differentiation (HYPAD) Lecture Notes The following tabs contains lecture notes on hypercomplex automatic differentiation. Complex Step Lecture Notes Derivation Closed Form Special Functions Step Size Study Numerical Integration Newton Rhapson ODE Solver CR Format 2nd Order Dual Lecture Notes Derivation Closed Form Step Size Study Numerical Integration Newton Rhapson ODE Solver CR Format [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/\" \/>\n<meta property=\"og:site_name\" content=\"HYPercomplex Automatic Differentiation\" \/>\n<meta property=\"article:modified_time\" content=\"2024-04-12T19:18:38+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/lecture-notes\\\/\",\"url\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/lecture-notes\\\/\",\"name\":\"Lecture Notes - HYPercomplex Automatic Differentiation\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#website\"},\"datePublished\":\"2023-07-17T17:53:32+00:00\",\"dateModified\":\"2024-04-12T19:18:38+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/lecture-notes\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/lecture-notes\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/lecture-notes\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lecture Notes\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#website\",\"url\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/\",\"name\":\"HYPercomplex Automatic Differentiation\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#organization\",\"name\":\"UTSA College of Engineering\",\"url\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/wp-content\\\/uploads\\\/sites\\\/50\\\/2020\\\/12\\\/cropped-cropped-HYPAD-Logo-e1716582453721.png\",\"contentUrl\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/wp-content\\\/uploads\\\/sites\\\/50\\\/2020\\\/12\\\/cropped-cropped-HYPAD-Logo-e1716582453721.png\",\"width\":511,\"height\":511,\"caption\":\"UTSA College of Engineering\"},\"image\":{\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Lecture Notes - HYPercomplex Automatic Differentiation","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/","og_locale":"en_US","og_type":"article","og_title":"Lecture Notes - HYPercomplex Automatic Differentiation","og_description":"Hypercomplex Automatic Differentiation (HYPAD) Lecture Notes The following tabs contains lecture notes on hypercomplex automatic differentiation. Complex Step Lecture Notes Derivation Closed Form Special Functions Step Size Study Numerical Integration Newton Rhapson ODE Solver CR Format 2nd Order Dual Lecture Notes Derivation Closed Form Step Size Study Numerical Integration Newton Rhapson ODE Solver CR Format [&hellip;]","og_url":"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/","og_site_name":"HYPercomplex Automatic Differentiation","article_modified_time":"2024-04-12T19:18:38+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/","url":"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/","name":"Lecture Notes - HYPercomplex Automatic Differentiation","isPartOf":{"@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#website"},"datePublished":"2023-07-17T17:53:32+00:00","dateModified":"2024-04-12T19:18:38+00:00","breadcrumb":{"@id":"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/lecture-notes\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/ceid.utsa.edu\/HYPAD\/"},{"@type":"ListItem","position":2,"name":"Lecture Notes"}]},{"@type":"WebSite","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#website","url":"https:\/\/ceid.utsa.edu\/HYPAD\/","name":"HYPercomplex Automatic Differentiation","description":"","publisher":{"@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/ceid.utsa.edu\/HYPAD\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#organization","name":"UTSA College of Engineering","url":"https:\/\/ceid.utsa.edu\/HYPAD\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#\/schema\/logo\/image\/","url":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2020\/12\/cropped-cropped-HYPAD-Logo-e1716582453721.png","contentUrl":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2020\/12\/cropped-cropped-HYPAD-Logo-e1716582453721.png","width":511,"height":511,"caption":"UTSA College of Engineering"},"image":{"@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/pages\/491","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/users\/248"}],"replies":[{"embeddable":true,"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/comments?post=491"}],"version-history":[{"count":0,"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/pages\/491\/revisions"}],"wp:attachment":[{"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/media?parent=491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}