{"page":"<link rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-572d6a42.css\" />\n<link rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-f4d0de30.css\" media=\"all\" />\n<div data-title='But what is a Fourier series? From heat flow to circle drawings: Differential Equations - Part 4 0f 5' data-url='/boclips/videos/5de51ed7832c7977e57bf696' data-video-url='/boclips/videos/5de51ed7832c7977e57bf696' id='bo_player_modal'>\n<div class='boclips-resource-page modal-dialog panel-container'>\n<div class='react-notifications-root'></div>\n<div class='rp-header'>\n<div class='rp-type'>\n<i aria-hidden='true' class='fai fa-regular fa-circle-play'></i>\nVideo\n</div>\n<h1 class='rp-title' id='video-title'>\nBut what is a Fourier series? From heat flow to circle drawings: Differential Equations - Part 4 0f 5\n</h1>\n<div class='rp-actions'>\n<div class='mr-1'>\n<a class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"><span><span>Get Free Access</span><span class=\"\"> for 10 Days</span><span>!</span></span></a>\n</div>\n</div>\n</div>\n<div class='rp-body'>\n<div class='rp-info'>\n<div aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'>&times;</div>\n<i aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'></i>\n<i aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'></i>\n<div class='rp-rating'>\n<span class='resource-pool'>\n<span class='pool-label'>Publisher:</span>\n<span class='pool-name'>\n<span class='text'><a data-publisher-id=\"30354888\" href=\"/search?publisher_ids%5B%5D=30354888\">3Blue1Brown</a></span>\n</span>\n</span>\n</div>\n<div class='rp-description'>\n<span class='short-description'>Fourier series, from the heat equation to sines to cycles.</span>\n<span class='full-description hide'>Fourier series, from the heat equation to sines to cycles.</span>\n</div>\n<div class='rp-report'>\n</div>\n<div aria-labelledby='resource-details-heading' class='rp-info-section'>\n<h2 class='title' id='resource-details-heading'>Resource Details</h2>\n<div class='rp-resource-details clearfix'>\n<div class='detail'>\n<dl>\n<dt>Curator Rating</dt>\n<dd><span class=\"star-rating\" aria-label=\"5.0 out of 5 stars\" role=\"img\"><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i></span></dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt class=\"educator-rating-title\">Educator Rating</dt><dd><div class=\"educator-rating-details\" data-path=\"/educator_ratings/rrp_data?resourceable_id=210833&amp;resourceable_type=Boclips%3A%3AVideoMetadata\"><span class=\"not-yet-rated\">Not yet Rated</span></div></dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Media Length</dt>\n<dd>24:14</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Grade</dt><dd title=\"Grade\">12th - Higher Ed</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Subjects</dt><dd><span><a href=\"/search?grade_ids%5B%5D=258&amp;grade_ids%5B%5D=259&amp;search_tab_id=1&amp;subject_ids%5B%5D=365220\">Math</a></span></dd><dd class=\"text-muted\"><i class=\"fa-solid fa-lock mr5\"></i>7 more...</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Media Type</dt><dd><span><a href=\"/search?grade_ids%5B%5D=258&amp;grade_ids%5B%5D=259&amp;search_tab_id=2&amp;type_ids%5B%5D=4543647\">Instructional Videos</a></span></dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Source:</dt>\n<div class='preview-source' data-animation='true' data-boundary='.rp-info' data-container='.rp-resource-details' data-html='false' data-title='3Blue1Brown is a channel about visualizing math, with content ranging from calculus to linear algebra, topology, neural networks and even how bitcoin works.' data-trigger='hover focus'>\n<span>3Blue1Brown</span>\n<i aria-hidden='true' class='fa-solid fa-circle-info channel-tooltip-icon' id='channel-tooltip'></i>\n</div>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Date</dt>\n<dd>2019</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<i aria-hidden='true' class='fai fa-solid fa-language'></i>\n<dt>Language</dt><dd>English</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Audiences</dt><dd><span><a href=\"/search?audience_ids%5B%5D=371079&amp;grade_ids%5B%5D=258&amp;grade_ids%5B%5D=259&amp;search_tab_id=1\">For Teacher Use</a></span></dd><dd class=\"text-muted\"><i class=\"fa-solid fa-lock mr5\"></i>2 more...</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Usage Permissions</dt><dd>Fine Print: Educational Use</dd>\n</dl>\n</div>\n</div>\n</div>\n<div aria-labelledby='additional-materials-heading' class='rp-info-section'>\n<h2 class='title' id='additional-materials-heading'>Additional Materials</h2>\n<div class='additional-material'>\n<i aria-hidden='true' class='fai fa-solid fa-lock'></i>\n<a class=\"text-muted\" title=\"Video Transcript\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"<div class=&quot;text-center py-2&quot;><a class=&quot;bold&quot; href=&quot;/auth/users/sign_in&quot;>Sign in</a> or <a class=&quot;bold text-danger&quot; data-posthog-event=&quot;Signup: LP Signup Activity&quot; data-posthog-location=&quot;body_link_boclips&quot; data-remote=&quot;true&quot; href=&quot;/subscription/new&quot;>Join Now</a></div>\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" href=\"/subscription/new\">Video Transcript</a>\n</div>\n<div class='additional-material'>\n<i aria-hidden='true' class='fai fa-solid fa-lock'></i>\n<a class=\"text-muted\" title=\"Video Preview\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"<div class=&quot;text-center py-2&quot;><a class=&quot;bold&quot; href=&quot;/auth/users/sign_in&quot;>Sign in</a> or <a class=&quot;bold text-danger&quot; data-posthog-event=&quot;Signup: LP Signup Activity&quot; data-posthog-location=&quot;body_link_boclips&quot; data-remote=&quot;true&quot; href=&quot;/subscription/new&quot;>Join Now</a></div>\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" href=\"/subscription/new\">Video Preview</a>\n</div>\n</div>\n<div aria-labelledby='concepts-heading' class='rp-info-section'>\n<h2 class='title' id='concepts-heading'>Concepts</h2>\n<div class='clearfix'>\n<div class='details-list concepts' data-identifier='Boclips::VideoDecorator5de51ed7832c7977e57bf696' data-type='concepts'>differential equations, waves, vector, sine, frequency, series</div>\n<div class='concepts-toggle-buttons' data-identifier='Boclips::VideoDecorator5de51ed7832c7977e57bf696'>\n<button aria-expanded='false' class='more btn-link' type='button'>\n<span>Show More</span>\n<i aria-hidden='true' class='fa-solid fa-caret-down ml5'></i>\n</button>\n<button aria-expanded='true' class='less btn-link' style='display: none;' type='button'>\n<span>Show Less</span>\n<i aria-hidden='true' class='fa-solid fa-caret-up ml5'></i>\n</button>\n</div>\n</div>\n</div>\n<div aria-labelledby='additional-tags-heading' class='rp-info-section'>\n<h2 class='title' id='additional-tags-heading'>Additional Tags</h2>\n<div class='clearfix'>\n<div class='details-list keyterms' data-identifier='Boclips::VideoDecorator5de51ed7832c7977e57bf696' data-type='keyterms'>general, complex number, complex constant, fourier series, vector hold, general formula, cosine waves, opposite directions, infinite family, vector rotating, special case, boundary condition, initial distribution, initial angle, square root, input range, infinite sum, sine wave, initial size, step function, mathematics, constant, constant vector, physics, evolve overtime, heat equation, rotating, broader context, constant term, arbitrarily close, higher frequency, cosine functions, rotating vectors, infinite, complex, step, wave</div>\n<div class='keyterms-toggle-buttons' data-identifier='Boclips::VideoDecorator5de51ed7832c7977e57bf696'>\n<button aria-expanded='false' class='more btn-link' type='button'>\n<span>Show More</span>\n<i aria-hidden='true' class='fa-solid fa-caret-down ml5'></i>\n</button>\n<button aria-expanded='true' class='less btn-link' style='display: none;' type='button'>\n<span>Show Less</span>\n<i aria-hidden='true' class='fa-solid fa-caret-up ml5'></i>\n</button>\n</div>\n</div>\n</div>\n<div aria-labelledby='classroom-considerations-heading' class='rp-info-section'>\n<h2 class='title' id='classroom-considerations-heading'>Classroom Considerations</h2>\n<div class='classroom-considerations'><div class='fai fa-solid fa-bell'></div>Best For: Explaining a topic</div><div class='classroom-considerations'><div class='fai fa-solid fa-bell'></div>Video is ad-free</div> \n</div>\n<div aria-labelledby='educator-ratings-heading' class='rp-info-section'>\n<h2 class='title sr-only' id='educator-ratings-heading'>Educator Ratings</h2>\n<div id=\"educator-ratings-root\"></div><div id=\"all-educator-ratings-root\"></div><div id=\"educator-rating-form-root\"></div>\n</div>\n</div>\n<div class='rp-resource'>\n<div aria-label='Show resource details' class='rp-show-info' role='button' tabindex='0'>\n<i class='fai fa-solid fa-align-left'></i>\nShow resource details\n</div>\n<div aria-label='Video player' class='player' id='player-wrapper' role='region'>\n<div class='relative container mx-auto' id='lp-boclips-visitor-thumbnail'>\n<a class=\"block\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"<div class=&quot;text-center py-2&quot;><a class=&quot;bold&quot; 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