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(00:00-01:19) Chapter 1: Manifolds (00:01:19-00:10:35) https://dibeos.net/2025/04/12/how-to-... Chapter 2: How to do Calculus on manifolds (00:10:35-00:19:04)...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2298643/c4fffb34ebd78f1e5773540076169513/564x318_1"},"target":"_self","position":"10","reqid":"1773446603493287-13279437002171625230-balancer-l7leveler-kubr-yp-vla-107-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DEllUe_5ZGyM","linkTemplate":"/video/preview/15032566225873250986?parent-reqid=1773446603493287-13279437002171625230-balancer-l7leveler-kubr-yp-vla-107-BAL&text=DIBEOS&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"The Mathematics of General Relativity","related_orig_text":"DIBEOS","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"DIBEOS\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=EllUe_5ZGyM\",\"src\":\"serp\",\"rvb\":\"EqwDChM5MDUzNzI3ODI4NDM3MzA2NDgzChQxMDU4NDYyOTY0MzgxMDQ5MjE0MAoUMTE0Nzg2NTgzMTM3MzkzNjg5NDIKEzgwNjU3MDM0MzEyNDUyMDI2MjMKEzQ2MTc0NzkyNzE1ODMzOTM2NjIKFDExMDcwNTIxMDg2NTQxNjY5NjI4ChQxMDg0MTEzMDExMzIzMjQ0MDI2NwoTNDQ0NjEwNTg2Mzg4MDI4MDc1MAoTNzMzNDg2MDY4NjIyNDA4Njc3MwoUMTUwMzI1NjYyMjU4NzMyNTA5ODYKEzgwNTI1MTc0NjgxNTA0NjQ3MjkKFDEzNDE4NDUwMDIwMjQ0Njc0OTM2ChQxMjE3NjYwMjg1MDk4MDgyMjQ3NgoUMTIzNzkwMzgzODU0NDQxNTQ3ODcKEzYxMzUwMTk0MDgwMTU5OTA2MjcKEzQ1NzExMjU4Mzg2NjUwNzgyOTgKEzgxNDM5MTc4NDMxNjcwNzc0ODQKFDE2ODQxMTk5MzU4MTI5OTQyOTc2ChM2Nzk1ODg4MTIwODMzNDQyNjU2ChIzNjcyMTU0MDA0MDQ0NTI4MDUaFgoUMTUwMzI1NjYyMjU4NzMyNTA5ODZaFDE1MDMyNTY2MjI1ODczMjUwOTg2aq4NEgEwGAAiRBowAAopaGh2ZGtqYW9menNza2FxaGhVQzNaMXJYQ0ZGYWRIdzY5LVBacFFSWVESAgARKhDCDw8aDz8T-n-CBCQBgAQrKosBEAEaeIH0CPsH_QMA8AUMBRAD_QD1E_T8-P39APYH_P7_Av8A8gIO-gcAAAAKFAEJ_gAAAPj9BwP8_wAACPz1_fgAAAAc-gL1_QAAABoR_wD-AQAA9fL_AQP_AAARCQgB_wAAAPv9Av39_gAABAgDBAAAAAD7_gz-_wAAACAALSM_3Ds4E0AJSE5QAipzEAAaYO8OAEoQGOK_DC3q6_rq_wjxAPEE0vMA5_QA-jIDxRcnAN8eCgAm6yD0ugAAACzVBf7LAMJXx9jiCxo_EuTlEwsHfxn97RYLFP_6_ef65PEZCNC_6ADSA_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_AAAAQAAAYEEAAFBCAACIwQAAEEEAAGBCAAAAwgAA4EAAAEjCAACowQAA6MEAAJTCAACAQAAAeEIAAPhBAACAQQAAJMIAACDCAACYQQAAqMEAAMjBAAAAwQAAHEIAAKhBAADIwQAAwMEgADgTQAlIdVABKo8CEAAagAIAABS-AADIPQAAQDwAAFQ-AACCvgAApj4AAHA9AAAtvwAA6r4AAJg9AACOvgAAHL4AAHy-AAA8PgAAqL0AAKq-AADYPQAAED0AAAU_AAAJPwAAfz8AAHS-AADKPgAAUD0AAIa-AAB0vgAAXL4AAMg9AADYPQAAlj4AAIY-AADKvgAAND4AAKA8AAAEvgAA-D0AAMg9AADmvgAAA78AAPi9AABMPgAAHL4AAGw-AAA8vgAAJL4AAAy-AACCPgAA2r4AAGy-AADqvgAAyL0AADy-AABkPgAAiD0AAOC8AAAMPgAAXz8AANg9AACYvQAAQLwAALi9AAD4PQAAJD4AAJK-IAA4E0AJSHxQASqPAhABGoACAABEvgAAjj4AAFA9AABLvwAA2L0AAGy-AAAEPgAABL4AAHw-AABEPgAAHD4AAOi9AADgPAAAbL4AAEC8AAAQPQAAiD0AAAs_AABQvQAAqj4AACS-AAAMPgAA6L0AABS-AACYvQAA6D0AAIC7AADoPQAA2L0AAFC9AACgPAAAHD4AAIA7AAAwvQAAEL0AAOC8AACAOwAA4DwAADS-AADgPAAAUL0AAHC9AAC6vgAAiD0AAI6-AACYvQAAf78AAHA9AAAUvgAAQDwAAKA8AABAPAAA2L0AACQ-AACoPQAA6D0AAFC9AACgvAAAgDsAAES-AAAsvgAAtr4AAMg9AAAsPiAAOBNACUh8UAEwCTgBSgBgAGgA\"}","related_url":"http://www.youtube.com/watch?v=EllUe_5ZGyM","parent-reqid":"1773446603493287-13279437002171625230-balancer-l7leveler-kubr-yp-vla-107-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["15032566225873250986"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":false,"contentTypeId":null,"censored":false,"censoredShock":false,"isShockDoc":false},"8052517468150464729":{"videoId":"8052517468150464729","docid":"34-11-3-ZCB95625E94421C09","description":"I might be helpful! 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