Electricity and Magnetism: Electrostatics

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="vertical" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-lesson5a-DD"> <h2 class="hd hd-2 unit-title">Intro: Gauss's Law Derivation</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@html-lesson5a-DD"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="html" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@html-lesson5a-DD"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <p> This is an optional sequence going through the derivation of the Gauss's Law. </p> </div> </div> </div> </div>

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<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="vertical" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L05DD02"> <h2 class="hd hd-2 unit-title">L5DD2: Flux Through a Closed Surface with Charge Outside</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD02"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="video" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD02"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L05DD02: Flux Through a Closed Surface with Charge Outside</h3> <div id="video_L05DD02" class="video closed" data-metadata='{"lmsRootURL": "https://openlearninglibrary.mit.edu", "poster": null, "transcriptLanguages": {"en": "English"}, "showCaptions": "true", "ytMetadataEndpoint": "", "completionEnabled": false, "streams": "1.00:nZRZbsY8vnI", "saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD02/handler/xmodule_handler/save_user_state", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD02/handler/transcript/translation/__lang__", "savedVideoPosition": 0.0, "end": 0.0, "captionDataDir": null, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD02/handler/publish_completion", "generalSpeed": 1.0, "autoAdvance": false, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD02/handler/transcript/available_translations", "start": 0.0, "duration": 0.0, "prioritizeHls": false, "autohideHtml5": false, "saveStateEnabled": false, "autoplay": false, "transcriptLanguage": "en", "completionPercentage": 0.95, "recordedYoutubeIsAvailable": true, "speed": null, "sources": [], "ytTestTimeout": 1500, "ytApiUrl": "https://www.youtube.com/iframe_api"}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L05DD02"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L05DD02">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L05DD02"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD02/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD02/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="vertical" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L05DD03"> <h2 class="hd hd-2 unit-title">L5DD3: Flux Through a More General Closed Surface with Charge Outside</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD03"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="video" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD03"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L05DD03: Flux Through a More General Closed Surface with Charge Outside</h3> <div id="video_L05DD03" class="video closed" data-metadata='{"lmsRootURL": "https://openlearninglibrary.mit.edu", "poster": null, "transcriptLanguages": {"en": "English"}, "showCaptions": "true", "ytMetadataEndpoint": "", "completionEnabled": false, "streams": "1.00:FZSD_EK1cAs", "saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD03/handler/xmodule_handler/save_user_state", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD03/handler/transcript/translation/__lang__", "savedVideoPosition": 0.0, "end": 0.0, "captionDataDir": null, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD03/handler/publish_completion", "generalSpeed": 1.0, "autoAdvance": false, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD03/handler/transcript/available_translations", "start": 0.0, "duration": 0.0, "prioritizeHls": false, "autohideHtml5": false, "saveStateEnabled": false, "autoplay": false, "transcriptLanguage": "en", "completionPercentage": 0.95, "recordedYoutubeIsAvailable": true, "speed": null, "sources": [], "ytTestTimeout": 1500, "ytApiUrl": "https://www.youtube.com/iframe_api"}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L05DD03"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L05DD03">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L05DD03"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD03/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD03/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="vertical" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L05DD04"> <h2 class="hd hd-2 unit-title">L5DD4: Flux Through a Generic Surface with No Enclosed Charge</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD04"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="video" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD04"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L05DD04: Flux Through a Generic Surface with No Enclosed Charge</h3> <div id="video_L05DD04" class="video closed" data-metadata='{"lmsRootURL": "https://openlearninglibrary.mit.edu", "poster": null, "transcriptLanguages": {"en": "English"}, "showCaptions": "true", "ytMetadataEndpoint": "", "completionEnabled": false, "streams": "1.00:mFAV-QzI0g8", "saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD04/handler/xmodule_handler/save_user_state", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD04/handler/transcript/translation/__lang__", "savedVideoPosition": 0.0, "end": 0.0, "captionDataDir": null, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD04/handler/publish_completion", "generalSpeed": 1.0, "autoAdvance": false, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD04/handler/transcript/available_translations", "start": 0.0, "duration": 0.0, "prioritizeHls": false, "autohideHtml5": false, "saveStateEnabled": false, "autoplay": false, "transcriptLanguage": "en", "completionPercentage": 0.95, "recordedYoutubeIsAvailable": true, "speed": null, "sources": [], "ytTestTimeout": 1500, "ytApiUrl": "https://www.youtube.com/iframe_api"}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L05DD04"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L05DD04">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L05DD04"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD04/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD04/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="vertical" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L05DD05"> <h2 class="hd hd-2 unit-title">L5DD5: Flux Through an Arbitrary Surface with One Point Charge Enclosed</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD05"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="video" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD05"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L05DD05: Flux Through an Arbitrary Surface with One Point Charge Enclosed</h3> <div id="video_L05DD05" class="video closed" data-metadata='{"lmsRootURL": "https://openlearninglibrary.mit.edu", "poster": null, "transcriptLanguages": {"en": "English"}, "showCaptions": "true", "ytMetadataEndpoint": "", "completionEnabled": false, "streams": "1.00:ojE2GGZevSM", "saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD05/handler/xmodule_handler/save_user_state", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD05/handler/transcript/translation/__lang__", "savedVideoPosition": 0.0, "end": 0.0, "captionDataDir": null, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD05/handler/publish_completion", "generalSpeed": 1.0, "autoAdvance": false, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD05/handler/transcript/available_translations", "start": 0.0, "duration": 0.0, "prioritizeHls": false, "autohideHtml5": false, "saveStateEnabled": false, "autoplay": false, "transcriptLanguage": "en", "completionPercentage": 0.95, "recordedYoutubeIsAvailable": true, "speed": null, "sources": [], "ytTestTimeout": 1500, "ytApiUrl": "https://www.youtube.com/iframe_api"}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L05DD05"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L05DD05">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L05DD05"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD05/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD05/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="vertical" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="VerticalStudentView" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L05DD06"> <h2 class="hd hd-2 unit-title">L5DD6: Flux Through an Arbitrary Surface with Many Point Charges Enclosed</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD06"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-request-token="f5d5d0b6ea7b11efbdc412d4917dea95" data-runtime-version="1" data-block-type="video" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-init="XBlockToXModuleShim" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD06"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L05DD06: Flux Through an Arbitrary Surface with Many Point Charges Enclosed</h3> <div id="video_L05DD06" class="video closed" data-metadata='{"lmsRootURL": "https://openlearninglibrary.mit.edu", "poster": null, "transcriptLanguages": {"en": "English"}, "showCaptions": "true", "ytMetadataEndpoint": "", "completionEnabled": false, "streams": "1.00:kqwAHUZmjxY", "saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD06/handler/xmodule_handler/save_user_state", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD06/handler/transcript/translation/__lang__", "savedVideoPosition": 0.0, "end": 0.0, "captionDataDir": null, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD06/handler/publish_completion", "generalSpeed": 1.0, "autoAdvance": false, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD06/handler/transcript/available_translations", "start": 0.0, "duration": 0.0, "prioritizeHls": false, "autohideHtml5": false, "saveStateEnabled": false, "autoplay": false, "transcriptLanguage": "en", "completionPercentage": 0.95, "recordedYoutubeIsAvailable": true, "speed": null, "sources": [], "ytTestTimeout": 1500, "ytApiUrl": "https://www.youtube.com/iframe_api"}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L05DD06"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L05DD06">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L05DD06"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD06/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L05DD06/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div>

To Use	Type	Examples
Numbers	Integers Fractions Decimals	2520 2/3 3.14, .98
Operators	+ - * / (add, subtract, multiply, divide) ^ (raise to a power) \|\| (parallel resistors)	x+(2*y)/x-1 x^(n+1) v_IN+v_OUT 1\|\|2
Constants	c, e, g, i, j, k, pi, q, T	20c 418T
Affixes	Percent sign (%) and metric affixes (d, c, m, u, n, p, k, M, G, T)	20% 20c 418T
Basic functions	abs, exp, fact or factorial, ln, log2, log10, sqrt	abs(x+y) sqrt(x^2-y)
Trigonometric functions	sin, cos, tan, sec, csc, cot arcsin, sinh, arcsinh, etc.	sin(4x+y) arccsch(4x+y)
Scientific notation	10^ and the exponent	10^-9
e notation	1e and the exponent	1e-9