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| comment | | "author":"mes",<br>"body":"<center>\n\n[![ (https:\/\/ipfs-3speak.b-cdn.net\/ipfs\/bafkreifjv2oaulyo6banb7txdxhqm2q4p2vaygsrjzoylml2iasbnriaoq\/) (https:\/\/3speak.tv\/watch?v=mes\/hndaankc)\n\n\u25b6\ufe0f [Watch on 3Speak (https:\/\/3speak.tv\/watch?v=mes\/hndaankc)\n\n<\/center>\n\n---\n\nIn this video I go over the water wave velocity equation and approximate it when the waves are deep and when the waves are shallow. For deep waves,<br> the hyperbolic tan or tanh(x) term in the water wave velocity equation approaches zero,<br> which greatly simplifies the equation. For shallow waves,<br> we can use the Maclaurin series approximation for tanh(x) and show that 3rd order or higher terms approach zero for shallow waves. I also calculate the error of this shallow wave speed approximation by using the alternating series estimation theorem.\r\n\r\nTimestamps:\r\n\r\n- Exercise 4: Water waves speed: 0:00\r\n- Solution to (a): Deep water wave speed approximation: 1:43\r\n - Approximation using hyperbolic tanh(x) = 1: 3:38\r\n - Deep wave speed approximation formula: 5:29\r\n- Solution to (b): Shallow water wave speed approximation: 6:04\r\n - Maclaurin series approximation for tanh(x): 7:05\r\n - Determining derivatives of tanh(x) at a = 0: 8:44\r\n - Writing out our Maclaurin series approximation of tanh(x): 17:18\r\n - 3rd order terms approach zero when water is shallow: 20:07\r\n - Shallow water speed approximation: 21:43\r\n - Shallow water speed approximation formula: 23:22\r\n- Solution to (c): Alternating Series Estimation Theorem for the error: 24:25\r\n - Estimation for tanh(x) approximation: 26:53\r\n - tanh(x) remainder approximation if L is greater than 10d: 30:00\r\n - Estimating accuracy of shallow water wave speed: 32:33\r\n - Error is less than 0.0132gL: 34:02\r\n\r\nFull video,<br> notes,<br> and playlists:\r\n\r\n- Full video and playlist: https:\/\/www.youtube.com\/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3\r\n- HIVE notes: https:\/\/peakd.com\/hive-128780\/@mes\/infinite-sequences-and-series-applications-of-taylor-polynomials\r\n- Infinite Sequences and Series: https:\/\/www.youtube.com\/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .\r\n\r\n------------------------------------------------------\r\n\r\nBecome a MES Super Fan! https:\/\/www.youtube.com\/channel\/UCUUBq1GPBvvGNz7dpgO14Ow\/join\r\n\r\nDONATE! \u0295 \u2022\u1d25\u2022\u0294 https:\/\/mes.fm\/donate\r\n\r\nSUBSCRIBE via EMAIL: https:\/\/mes.fm\/subscribe\r\n\r\nMES Links: https:\/\/mes.fm\/links\r\n\r\nMES Truth: https:\/\/mes.fm\/truth\r\nOfficial Website: https:\/\/MES.fm\r\nHive: https:\/\/peakd.com\/@mes\r\n\r\nEmail me: [email protected]\r\n\r\nFree Calculators: https:\/\/mes.fm\/calculators\r\n\r\nBMI Calculator: https:\/\/bmicalculator.mes.fm\r\nGrade Calculator: https:\/\/gradecalculator.mes.fm\r\nMortgage Calculator: https:\/\/mortgagecalculator.mes.fm\r\nPercentage Calculator: https:\/\/percentagecalculator.mes.fm\r\n\r\nFree Online Tools: https:\/\/mes.fm\/tools\r\n\r\niPhone and Android Apps: https:\/\/mes.fm\/mobile-apps\n\n---\n\n\u25b6\ufe0f [3Speak (https:\/\/3speak.tv\/watch?v=mes\/hndaankc)\n",<br>"json_metadata":" \"tags\":[\"math\",<br>\"science\",<br>\"physics\",<br>\"stemgeeks\",<br>\"stemsocial\",<br>\"palnet\",<br>\"proofofbrain\",<br>\"chessbrothers\",<br>\"education\",<br>\"water\",<br>\"engineering\",<br>\"waves\" ,<br>\"app\":\"3speak\/0.3.0\",<br>\"type\":\"3speak\/video\",<br>\"image\":[\"https:\/\/ipfs-3speak.b-cdn.net\/ipfs\/bafkreifjv2oaulyo6banb7txdxhqm2q4p2vaygsrjzoylml2iasbnriaoq\" ,<br>\"video\"<br>\"info\"<br>\"platform\":\"3speak\",<br>\"title\":\"Exercise 4: Approximating the Velocity of a Shallow Water Wave using Maclaurin Series\",<br>\"author\":\"mes\",<br>\"permlink\":\"hndaankc\",<br>\"duration\":2171.901678,<br>\"filesize\":159967060,<br>\"file\":\"ipfs:\/\/QmWExt4nzaH7x5eoSw8ZWZKTa5jgCJV5QiumsMZZVrJUA1\",<br>\"lang\":\"en\",<br>\"firstUpload\":false,<br>\"ipfs\":null,<br>\"ipfsThumbnail\":null,<br>\"video_v2\":\"ipfs:\/\/Qmah6NzTZAfh6SWasYA2nBXuH3CqR7aQ6JXjR8y9AEEQyJ\/manifest.m3u8\",<br>\"sourceMap\":[ \"type\":\"video\",<br>\"url\":\"ipfs:\/\/Qmah6NzTZAfh6SWasYA2nBXuH3CqR7aQ6JXjR8y9AEEQyJ\/manifest.m3u8\",<br>\"format\":\"m3u8\" ,<br> \"type\":\"thumbnail\",<br>\"url\":\"ipfs:\/\/bafkreifjv2oaulyo6banb7txdxhqm2q4p2vaygsrjzoylml2iasbnriaoq\" ,<br>\"content\"<br>\"description\":\"In this video I go over the water wave velocity equation and approximate it when the waves are deep and when the waves are shallow. For deep waves,<br> the hyperbolic tan or tanh(x) term in the water wave velocity equation approaches zero,<br> which greatly simplifies the equation. For shallow waves,<br> we can use the Maclaurin series approximation for tanh(x) and show that 3rd order or higher terms approach zero for shallow waves. I also calculate the error of this shallow wave speed approximation by using the alternating series estimation theorem.\\r\\n\\r\\nTimestamps:\\r\\n\\r\\n- Exercise 4: Water waves speed: 0:00\\r\\n- Solution to (a): Deep water wave speed approximation: 1:43\\r\\n - Approximation using hyperbolic tanh(x) = 1: 3:38\\r\\n - Deep wave speed approximation formula: 5:29\\r\\n- Solution to (b): Shallow water wave speed approximation: 6:04\\r\\n - Maclaurin series approximation for tanh(x): 7:05\\r\\n - Determining derivatives of tanh(x) at a = 0: 8:44\\r\\n - Writing out our Maclaurin series approximation of tanh(x): 17:18\\r\\n - 3rd order terms approach zero when water is shallow: 20:07\\r\\n - Shallow water speed approximation: 21:43\\r\\n - Shallow water speed approximation formula: 23:22\\r\\n- Solution to (c): Alternating Series Estimation Theorem for the error: 24:25\\r\\n - Estimation for tanh(x) approximation: 26:53\\r\\n - tanh(x) remainder approximation if L is greater than 10d: 30:00\\r\\n - Estimating accuracy of shallow water wave speed: 32:33\\r\\n - Error is less than 0.0132gL: 34:02\\r\\n\\r\\nFull video,<br> notes,<br> and playlists:\\r\\n\\r\\n- Full video and playlist: https:\/\/www.youtube.com\/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3\\r\\n- HIVE notes: https:\/\/peakd.com\/hive-128780\/@mes\/infinite-sequences-and-series-applications-of-taylor-polynomials\\r\\n- Infinite Sequences and Series: https:\/\/www.youtube.com\/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .\\r\\n\\r\\n------------------------------------------------------\\r\\n\\r\\nBecome a MES Super Fan! https:\/\/www.youtube.com\/channel\/UCUUBq1GPBvvGNz7dpgO14Ow\/join\\r\\n\\r\\nDONATE! \u0295 \u2022\u1d25\u2022\u0294 https:\/\/mes.fm\/donate\\r\\n\\r\\nSUBSCRIBE via EMAIL: https:\/\/mes.fm\/subscribe\\r\\n\\r\\nMES Links: https:\/\/mes.fm\/links\\r\\n\\r\\nMES Truth: https:\/\/mes.fm\/truth\\r\\nOfficial Website: https:\/\/MES.fm\\r\\nHive: https:\/\/peakd.com\/@mes\\r\\n\\r\\nEmail me: [email protected]\\r\\n\\r\\nFree Calculators: https:\/\/mes.fm\/calculators\\r\\n\\r\\nBMI Calculator: https:\/\/bmicalculator.mes.fm\\r\\nGrade Calculator: https:\/\/gradecalculator.mes.fm\\r\\nMortgage Calculator: https:\/\/mortgagecalculator.mes.fm\\r\\nPercentage Calculator: https:\/\/percentagecalculator.mes.fm\\r\\n\\r\\nFree Online Tools: https:\/\/mes.fm\/tools\\r\\n\\r\\niPhone and Android Apps: https:\/\/mes.fm\/mobile-apps\",<br>\"tags\":[\"math\",<br>\"science\",<br>\"physics\",<br>\"stemgeeks\",<br>\"stemsocial\",<br>\"palnet\",<br>\"proofofbrain\",<br>\"chessbrothers\",<br>\"education\",<br>\"water\",<br>\"engineering\",<br>\"waves\" ",<br>"parent_author":"",<br>"parent_permlink":"hive-128780",<br>"permlink":"hndaankc",<br>"title":"Exercise 4: Approximating the Velocity of a Shallow Water Wave using Maclaurin Series" | | comment_options | "allow_curation_rewards":true,
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