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Line Integrals and Vector Fields

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    ืื—ื“ ื”ืจืขื™ื•ื ื•ืช ื”ื‘ืกื™ืกื™ื™ื ื‘ื™ื•ืชืจ ื‘ืคื™ื–ื™ืงื”
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    ื”ื•ื ื”ืจืขื™ื•ืŸ ืฉืœ ืขื‘ื•ื“ื”.
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    ื›ืขืช, ื›ืฉืœืจืืฉื•ื ื” ืืชื” ืœื•ืžื“ ืœืขื‘ื•ื“, ืืชื” ืื•ืžืจ ืœืขืฆืžืš, ื‘ืกื“ืจ, ื–ื”
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    ืจืง ื›ื•ื— ื”ืชืœื•ื™ ื‘ืžืจื—ืง.
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    ืื‘ืœ ืื–, ืื—ืจ ื›ืš, ื›ืฉืืชื ืœื•ืžื“ื™ื ืงืฆืช ืขืœ
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    ื•ืงื˜ื•ืจื™ื, ืืชื ืžื‘ื™ื ื™ื ืฉื”ื›ื•ื— ืœื ืชืžื™ื“ ื”ื•ืœืš ื™ื—ื“
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    ื‘ืื•ืชื• ื›ื•ื•ืŸ ืฉืœ ื”ืชื ื•ืขื”.
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    ืื– ืืชื ืœื•ืžื“ื™ื ืฉืœืขื‘ื•ื“ื” ื™ืฉ ื—ืฉื™ื‘ื•ืช. ืชืŸ ืœื™
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    ืœืจืฉื•ื ื–ืืช: ื”ื’ื•ื“ืœ ืฉืœ ื”ื›ื•ื—,
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    ืื• ื”ืžืจื›ื™ื‘ ืฉืœ ื”ื›ื•ื—, ื‘ื›ื™ื•ื•ืŸ
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    ืฉืœ ื”ืชื ื•ืขื”.
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    ืชื ื•ืขื” ื–ื” ืจืง ืžืจื—ืง ืขื ืงืฆืช ื›ื™ื•ื•ืŸ.
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    ืื ืžื’ื“ื™ืœื™ื ืืช ื”ืชื ื•ืขื”, ืื– ื ื™ืชืŸ ืœื”ื’ื™ื“
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    ืฉื”ื’ื“ื™ืœื• ืืช ื”ืžืจื—ืง ืฉืขื‘ืจ ื”ื’ื•ืฃ.
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    ื•ื”ื ื” ื“ื•ื’ืžื ืงืœืืกื™ืช:
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    ืื•ืœื™ ื™ืฉ ืœื›ื ืงื•ื‘ื™ื™ืช ืงืจื—, ืื• ืื™ื–ื• ื‘ืœื˜ื”.
  • 1:06 - 1:09
    ืื• ืจืง ืงืจื—, ื›ื™ ืฉืœื ื™ื”ื™ื” ื”ืจื‘ื” ื—ื™ื›ื•ืš.
  • 1:09 - 1:13
    ืื•ืœื™ ื–ื” ืฆืฃ ืขืœ ืื’ื ื’ื“ื•ืœ ืื• ืขืœ ื’ื‘ื™ ืงืจื—ื•ืŸ ืื• ืžืฉื”ื• ื“ื•ืžื”.
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    ื•ื™ื™ืชื›ืŸ ืฉืืชื ื“ื•ื—ืคื™ื ืืช ืงื•ื‘ื™ืช ื”ืงืจื— ื”ื–ื• ื‘ื–ื•ื•ื™ืช.
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    ื‘ื•ืื• ื ื’ื™ื“, ืฉืืชื ื™ื•ืฆืจื™ื ื–ื•ื•ื™ืช ื‘ืื•ืคืŸ ื›ื–ื”.
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    ื–ื” ื”ื›ื•ื—, ืžืžืฉ ื›ืืŸ!
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    ื‘ื•ืื• ื ื’ื™ื“ ืฉื”ื›ื•ื— ืฉื•ื•ื”, ืื•ืงื™ ื–ื”
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    ื•ืงื˜ื•ืจ ื”ื›ื•ื— ืฉืœื ื•
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    ื‘ื•ืื• ื ื’ื™ื“ ืฉื”ื’ื•ื“ืœ ืฉืœ ื•ืงื˜ื•ืจ ื”ื›ื•ื—, ื ื’ื™ื“...
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    10 ื ื™ื•ื˜ื•ืŸ.
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    ื•ื‘ื•ืื• ื ื’ื™ื“ ืฉื”ื›ื•ื•ืŸ ืฉืœ ื•ืงื˜ื•ืจ ื”ื›ื•ื—, ืื•ืงื™,
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    ืœื›ืœ ื•ืงื˜ื•ืจ ื™ืฉ ื›ื™ื•ื•ืŸ ื•ื’ื•ื“ืœ,
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    ื•ืœื’ื‘ื™ ื”ื›ื•ื•ืŸ, ื‘ื•ืื• ื ื’ื™ื“ ืฉื™ืฉ ืœื• ื–ื•ื•ื™ืช ืฉืœ 30 ืžืขืœื•ืช, ื›ืœื•ืžืจ 60 ืžืขืœื•ืช
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    ืžืขืœ ื”ืื•ืคืง.
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    ืื– ื–ื” ื”ื›ื•ื•ืŸ ืฉืื ื™ ื“ื•ื—ืฃ ืืœื™ื•.
  • 1:50 - 1:53
    ื•ื‘ื•ืื• ื ื’ื™ื“ ืฉืื ื™ ืžื–ื™ื– ืืช ื–ื”.
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    ื–ื” ื”ื›ืœ ื—ื–ืจื”, ืื ื™ ืžืงื•ื•ื”.
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    ืื ืืชื ืžื–ื™ื–ื™ื ืืช ื–ื”, ื‘ื•ืื• ื ื’ื™ื“ ืฉืืชื ืžื–ื™ื–ื™ื ืืช ื–ื” ื‘ื›ื•ื— ืฉืœ 5 ื ื™ื•ื˜ื•ืŸ.
  • 1:59 - 2:03
    ืื– ื‘ื•ืื• ื ื’ื™ื“ ืฉื”ืชื ื•ืขื”, ื–ื” ื•ืงื˜ื•ืจ ื”ืชื ื•ืขื”
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    ืžืžืฉ ื›ืืŸ, ื•ื”ื’ื•ื“ืœ ืฉืœื• ืฉื•ื•ื” ืœ5 ืžื˜ืจื™ื.
  • 2:10 - 2:13
    ืื– ืœืžื“ืชื ืžื”ื’ื“ืจืช ื”ืขื‘ื•ื“ื”, ืฉืืชื ืœื ื™ื›ื•ืœื™ื
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    ื‘ื•ืื• ื ื’ื™ื“, ืื”ื”ื”, ืื ื™ ื“ื•ื—ืฃ ืขื ื›ื•ื— ืฉืœ 10 ื ื™ื•ื˜ื•ืŸ
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    ื•ื–ื” ื–ื– 5 ืžื˜ืจื™ื.
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    ืืชื ื™ื›ื•ืœื™ื ืคืฉื•ื˜ ืœื”ื›ืคื™ืœ ืืช ืขืฉืจืช ื”ื ื™ื•ื˜ื•ื ื™ื 5 ืคืขืžื™ื (ืคืขื ืื—ืช ืœื›ืœ ืžื˜ืจ)
  • 2:23 - 2:26
    ืืชื ืฆืจื™ื›ื™ื ืœืžืฆื•ื ืืช ื”ื’ื•ื“ืœ ืฉืœ ื”ืจื›ื™ื‘
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    ืฉื ืžืฆื ื‘ืื•ืชื• ื”ื›ื•ื•ืŸ ื›ืžื• ืฉืœ ื”ืชื ื•ืขื”.
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    ืื– ืžื” ืฉืœืžืขืฉื” ืื ื™ ืฆืจื™ืš ืœืขืฉื•ืช ื”ื•ื, ื”ืื•ืจืš, ืื ืืชื”
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    ืžื“ืžื™ื™ืŸ ืืช ื”ืื•ืจืš ืฉืœ ื”ื•ืงื˜ื•ืจ ื”ื–ื” ื›-10, ื–ื”
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    ื”ื›ื•ื— ื”ื›ื•ืœืœ, ืื‘ืœ ืืชื ืฆืจื™ื›ื™ื ืœื’ืœื•ืช ืืช ื”ืื•ืจืš ืฉืœ
  • 2:38 - 2:41
    ื”ื•ืงื˜ื•ืจ, ื–ื” ืœืžืขืฉื” ื”ืจื›ื™ื‘ ืฉืœ ื”ื›ื•ื—, ืฉื”ื•ืœืš ื‘ืื•ืชื•
  • 2:41 - 2:43
    ื”ื›ื•ื•ืŸ ื›ืžื• ืฉืœ ื”ืชื ื•ืขื”.
  • 2:43 - 2:46
    ืขื ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื” ืคืฉื•ื˜ื”, ืืชื ื™ื•ื“ืขื™ื
  • 2:46 - 2:53
    ืฉื–ื” 10 ืคืขืžื™ื ื”ืงื•ืกื™ื ื•ืก ืฉืœ 60 ืžืขืœื•ืช, ืฉื–ื” ืฉื•ื•ื”
  • 2:53 - 2:58
    (ืงื•ืกื™ื ื•ืก ืฉืœ 60 ื–ื” ื—ืฆื™) ื•ืœื›ืŸ ื”ืชื•ืฆืื” ื”ื™ื 5.
  • 2:58 - 3:00
    ืื– ื”ื’ื•ื“ืœ ื”ื–ื”, ื”ื’ื•ื“ืœ ืฉืœ ื”ื›ื•ื— ืฉื”ื•ืœืš
  • 3:00 - 3:02
    ื‘ืื•ืชื• ื”ื›ื•ื•ืŸ ืฉืœ ื”ืชื ื•ืขื”
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    ื‘ืžืงืจื” ื”ื–ื”, ื”ื•ื 5 ื ื™ื•ื˜ื•ืŸ.
  • 3:05 - 3:08
  • 3:08 - 3:10
    ื•ื›ืขืช ื ื™ืชืŸ ืœื’ืœื•ืช ืžื”ื™ ื”ืขื‘ื•ื“ื”.
  • 3:10 - 3:20
    ืืชื ื™ื›ื•ืœื™ื ืœื”ื’ื™ื“ ืฉืขื‘ื•ื“ื” ืฉื•ื•ื” ืœ5 ื ื™ื•ื˜ื•ืŸ
  • 3:20 - 3:21
    (ื•ื ืจืฉื•ื ื ืงื•ื“ื” ืœื–ืžืŸ ืขื‘ื•ืจ ื”ื›ืคืœ)
  • 3:21 - 3:22
    ืื ื™ ืœื ืจื•ืฆื” ืฉืชื—ืฉื‘ื• ืฉืชื—ืฉื‘ื• ืฉื”ื›ื•ื•ื ื” ืœืžื›ืคืœื” ื•ืงื˜ื•ืจื™ืช
  • 3:22 - 3:27
    ื›ืคื•ืœ 5 ืžื˜ืจื™ื, ืฉื–ื” 25 ื ื™ื•ื˜ื•ืŸ ื›ืคื•ืœ ืžื˜ืจ. ืื• ืฉื ื™ืชืŸ ืœื”ื’ื™ื“
  • 3:27 - 3:31
    25 ื’'ืื•ืœ ืฉืœ ืขื‘ื•ื“ื” ื”ื•ืฉืงืขื•.
  • 3:31 - 3:35
    ื•ื›ืœ ื–ื” ื—ื–ืจื” ื‘ืกื™ืกื™ืช ื‘ืคื™ื–ื™ืงื”.
  • 3:35 - 3:37
    ืื‘ืœ ืจืง ืชื—ืฉื‘ื• ืœืจื’ืข ืžื” ืงื•ืจื” ื›ืืŸ.
  • 3:37 - 3:37
    ืžื” ื”ื™ื™ืชื” ื”ืขื‘ื•ื“ื”?
  • 3:37 - 3:39
    ืื ืื ื™ ื›ื•ืชื‘ ื‘ืื•ืคืŸ ืžื•ืคืฉื˜
  • 3:39 - 3:43
    ื”ืขื‘ื•ื“ื” ืฉื•ื•ื” ืœื—ืžืฉืช ื”ื ื™ื•ื˜ื•ื ื™ื.
  • 3:43 - 3:47
    ื–ื” ื”ื™ื” ื”ื’ื•ื“ืœ ืฉืœ ื•ืงื˜ื•ืจ ื”ื›ื•ื—, ืื– ื–ื”
  • 3:47 - 3:53
    ื”ื’ื•ื“ืœ ืฉืœ ื•ืงื˜ื•ืจ ื”ื›ื•ื—, ื›ืคื•ืœ ื”ืงื•ืกื™ื ื•ืก ืฉืœ ื”ื–ื•ื•ื™ืช ื”ื–ื•.
  • 3:53 - 3:54
    ืื– ืืชื ื™ื•ื“ืขื™ื, ื‘ื•ืื• ื ืงืจื ืœื–ื•ื•ื™ืช ื”ื–ื• ื˜ื˜ื”.
  • 3:54 - 3:55
    ื‘ื•ืื• ื ื’ื™ื“ ื–ืืช ื‘ืื•ืคืŸ ื›ืœืœื™.
  • 3:55 - 3:58
    ืื– ื›ืคื•ืœ ื”ืงื•ืกื™ื ื•ืก ืฉืœ ื”ื–ื•ื•ื™ืช.
  • 3:58 - 4:02
    ื–ื” ื”ื’ื•ื“ืœ ืฉืœ ื”ื›ื•ื— ื‘ื›ื•ื•ืŸ ืฉืœ
  • 4:02 - 4:05
    ื”ืชื ื•ืขื”, ื”ืงื•ืกื™ื ื•ืก ืฉืœ ื”ื–ื•ื•ื™ืช ืฉื‘ื™ื ื™ื”ื, ื›ืคื•ืœ
  • 4:05 - 4:07
    ื”ื’ื•ื“ืœ ืฉืœ ื”ืžืจื—ืง.
  • 4:07 - 4:12
    ืื– ื›ืคื•ืœ ื”ื’ื•ื“ืœ ืฉืœ ื”ืžืจื—ืง.
  • 4:12 - 4:16
    ืื• ืื ืจืฆื™ืชื™ ืœืจืฉื•ื ื–ืืช ืžื—ื“ืฉ, ื”ื™ื™ืชื™ ื™ื›ื•ืœ ืœืจืฉื•ื ื–ืืช ืคืฉื•ื˜ ื›ืš,
  • 4:16 - 4:19
    ื”ื’ื•ื“ืœ ืฉืœ ื”ืžืจื—ืง ื›ืคื•ืœ ื”ื’ื•ื“ืœ ืฉืœ
  • 4:19 - 4:23
    ื”ื›ื•ื— ื›ืคื•ืœ ืงื•ืกื™ื ื•ืก ื˜ื˜ื”.
  • 4:23 - 4:27
    ื•ื™ืฉ ืœื™ ืžืกืคืจ ืกืจื˜ื•ื ื™ื ืฉืœ ื–ื”, ื‘ืชื•ืš ื”ืคืœื™ืœื™ืกื˜
  • 4:27 - 4:29
    ืฉืœ ืืœื’ื‘ืจื” ืœื™ื ื™ืืจื™ืช, ื‘ืชื•ืš ื”ืคืœื™ื™ืœื™ืกื˜ ืฉืœ ืคื™ื–ื™ืงื”, ืฉื ืื ื™ ืžื“ื‘ืจ ืขืœ
  • 4:29 - 4:32
    ื”ื”ื‘ื“ืœ ื‘ื™ืŸ ืžื›ืคืœื” ื•ืงื˜ื•ืจื™ืช ืœืžื›ืคืœื” ืกืงืœืจื™ืช ื•ื›ืœ ื–ื”, ืื‘ืœ
  • 4:32 - 4:40
    ื›ืืŸ ื–ื• ืžื›ืคืœื” ืกืงืœืจื™ืช ืฉืœ ื”ื•ืงื˜ื•ืจื™ื d ื• f.
  • 4:40 - 4:44
    ืื– ื‘ืื•ืคืŸ ื›ืœืœื™, ืื ืืชื ืžื ืกื™ื ืœืžืฆื•ื ืืช ื”ืขื‘ื•ื“ื” ืขื‘ื•ืจ ืชื ื•ืขื” ืฉื•ื•ืช ืชืื•ืฆื”
  • 4:44 - 4:47
    ื•ื™ืฉ ืœื›ื ื›ื•ื— ืงื‘ื•ืข, ืืชื ืคืฉื•ื˜ ืœื•ืงื—ื™ื ืืช
  • 4:47 - 4:49
    ื”ืžื›ืคืœื” ื”ืกืงืœืจื™ืช ืฉืœ ืฉื ื™ ื”ื•ืงื˜ื•ืจื™ื ื”ืœืœื•
  • 4:49 - 4:51
    ื•ืื ื”ืžื›ืคืœื” ื”ืกืงืœืจื™ืช ื”ื™ื ื“ืจืš ืฉืœื’ืžืจื™ ื–ืจื”
  • 4:51 - 4:54
    ืœื›ื, ืื ื™ ื—ื•ืฉื‘ ืฉืื ื™ ืืขืฉื” ืขื•ื“,
  • 4:54 - 4:56
    4 ืื• 5 ืกืจื˜ื•ื ื™ื ืขืœ ืžื›ืคืœื•ืช ืกืงืœืจื™ื•ืช, ื•ืขืœ ื”ื“ืจื›ื™ื ืฉื‘ื”,
  • 4:56 - 4:57
    ื•ืื™ืš ื–ื” ืžืฉืชืžืฉื™ื ื‘ื”.
  • 4:57 - 4:59
    ืื‘ืœ ืจืง ื›ื“ื™ ืœืชืช ืœื›ื ืžื•ืฉื’ ื›ืœืœื™ ื•ืื™ื ื˜ื•ืื™ืฆื™ื” ื ื›ื•ื ื”
  • 4:59 - 5:04
    ืขืœ ื”ืžื›ืคืœื” ื”ืกืงืœืจื™ืช, ืื– ื›ืืฉืจ ืื ื™ ืœื•ืงื— f ื›ืคื•ืœ d, ืื• d ื›ืคื•ืœ f,
  • 5:04 - 5:08
    ืžื” ืฉื–ื” ืื•ืžืจ ื–ื” ืฉืื ื™ ืžื›ืคื™ืœ ืืช ื”ื’ื•ื“ืœ,
  • 5:08 - 5:10
    ื˜ื•ื‘ ืื ื™ ื™ื›ื•ืœ ืคืฉื•ื˜ ืœืงืจื•ื ืืช ื–ื”.
  • 5:10 - 5:14
    ืื‘ืœ ื”ืจืขื™ื•ืŸ ืฉืœ ืžื›ืคืœื” ืกืงืœืจื™ืช, ื”ื•ื ืœืงื—ืช ืืช ื”ื’ื•ื“ืœ ืžื”ื•ืงื˜ื•ืจ
  • 5:14 - 5:17
    ืฉื”ื•ืœืš ื‘ืื•ืชื• ื”ื›ื™ื•ื•ืŸ ืฉืœ ื”ื•ื•ืงื˜ื•ืจ ื”ื–ื”,
  • 5:17 - 5:18
    ืžืงืจื” ื”ื–ื”, ื”ื’ื•ื“ืœ ื”ื–ื”.
  • 5:18 - 5:21
    ื•ืื– ืœื”ื›ืคื™ืœ ืืช ืฉื ื™ ื”ื’ื“ืœื™ื ื”ืœืœื•.
  • 5:21 - 5:22
    ื•ื–ื” ืžื” ืฉืขืฉื™ื ื• ืžืžืฉ ื›ืืŸ.
  • 5:22 - 5:26
    ืื– ื”ืขื‘ื•ื“ื” ื”ื•ืœื›ืช ืœื”ื™ื•ืช ื•ืงื˜ื•ืจ ื”ื›ื•ื—, ื›ืœื•ืžืจ ืœืงื—ืช ืืช
  • 5:26 - 5:29
    ื”ื—ืœืง ื”ืกืงืœืจื™ ืฉืœ ื•ืงื˜ื•ืจ ื”ื›ื•ื— ื›ืคื•ืœ ื•ืงื˜ื•ืจ ื”ืชื ื•ืขื”,
  • 5:29 - 5:31
    ื•ื–ื”, ื›ืžื•ื‘ืŸ, ืขืจืš ืกืงืœืจื™.
  • 5:31 - 5:33
    ืื– ืื ื—ื ื• ื ื“ื’ื™ื ืžืกืคืจ ื“ื•ื’ืžืื•ืช
  • 5:33 - 5:34
    ื•ืืชื ืชืจืื• ืฉื–ื” ื ื›ื•ืŸ.
  • 5:34 - 5:39
    ืื– ื›ืœ ื–ื” ื—ื–ืจื” ืขืœ ืคื™ืกื™ืงื” ื‘ืกื™ืกื™ืช ื•ื™ืกื•ื“ื™ืช ื‘ื™ื•ืชืจ.
  • 5:39 - 5:42
    ื›ืขืช ื‘ื•ืื• ื ื™ืงื— ื“ื•ื’ืžื ื™ื•ืชืจ ืžืกื•ื‘ื›ืช, ืื‘ืœ
  • 5:42 - 5:44
    ื”ื™ื ื‘ืืžืช ืžืชื‘ืกืกืช ืขืœ ืื•ืชื• ื”ืจืขื™ื•ืŸ.
  • 5:44 - 5:46
    ื‘ื•ืื• ื ื’ื“ื™ืจ ืฉื“ื” ื•ืงื˜ื•ืจื™.
  • 5:46 - 5:49
  • 5:49 - 5:51
    ืื– ื‘ื•ืื• ื ื’ื™ื“ ืฉื™ืฉ ืœื™ ืฉื“ื” ื•ืงื˜ื•ืจื™ f, ื•ืื ื—ื ื•
  • 5:51 - 5:54
    ื”ื•ืœื›ื™ื ืœื—ืฉื•ื‘ ืœืจื’ืข, ืžื” ื–ื” ืื•ืžืจ.
  • 5:54 - 5:59
    ื–ื• ืคื•ื ืงืฆื™ื” ืฉืœ X ื• Y, ื•ื–ื” ืฉื•ื•ื” ืœืกืงืœืจ ื›ืœืฉื”ื•.
  • 5:59 - 6:04
    ืจื›ื™ื‘ ื•ืงื˜ื•ืจื™ ืื•ืคืงื™, ื•ืขื•ื“ ืื™ื–ื•ืฉื”ื™ ืคื•ื ืงืฆื™ื” ืื—ืจืช, ืื•
  • 6:04 - 6:09
    ืจื›ื™ื‘ ื•ืงื˜ื•ืจื™ ืื ื›ื™, ื•ืขื•ื“ ืื™ื–ื•ืฉื”ื™ ืคื•ื ืงืฆื™ื” ืฉื•ื ื”, ืคื•ื ืงืฆื™ื”
  • 6:09 - 6:14
    ืกืงืœืจื™ืช ืฉืœ X ื•ืฉืœ Y, ื›ืคื•ืœ ื”ืจื›ื™ื‘ ื”ื•ื•ืงื˜ื•ืจื™ ื”ืื•ืคืงื™.
  • 6:14 - 6:16
    ืื– ืžื” ืžืฉื”ื• ื›ื–ื” ื™ื”ื™ื”?
  • 6:16 - 6:17
    ื–ื”ื• ืฉื“ื” ื•ืงื˜ื•ืจื™.
  • 6:17 - 6:20
    ื–ื”ื• ืฉื“ื” ื•ืงื˜ื•ืจื™ ื“ื• ืžืžื“ื™.
  • 6:20 - 6:21
    ืื ื—ื ื• ื‘ืžืจื—ืง X-Y.
  • 6:21 - 6:31
  • 6:31 - 6:36
    ืื• ืฉืืชื” ื™ื›ื•ืœ ืœื”ื’ื™ื“, ืขืœ R2.
  • 6:36 - 6:38
    ื‘ื›ืœ ืžืงืจื”, ืื ื™ ืœื ืจื•ืฆื” ืœื”ื™ื›ื ืก ื™ื•ืชืจ ืžื“ื™
  • 6:38 - 6:39
    ืœืชื•ืš ื”ื—ืœืง ื”ื–ื”.
  • 6:39 - 6:41
    ืื‘ืœ ืžื” ื–ื” ืขื•ืฉื”?
  • 6:41 - 6:47
    ืื•ืงื™, ืื ื”ื™ื™ืชื™ ืฆืจื™ืš ืœืฉืจื˜ื˜ ืืช ืžืจื—ืง X-Y ืฉืœื™, ืื– ืชื”ื™ื” ืœื™ ืฉื•ื‘
  • 6:47 - 6:49
    ื‘ืขื™ื” ืœืฉืจื˜ื˜ ืงื• ื™ืฉืจ.
  • 6:49 - 6:51
    ืื•ืงื™, ื”ื ื” ืื ื—ื ื• ืžืžืฉื™ื›ื™ื.
  • 6:51 - 6:54
    ื–ื” ืฆื™ืจ ื”Y ืฉืœื™, ื•ื–ื” ืฆื™ืจ ื”X ืฉืœื™.
  • 6:54 - 6:56
    ืื ื™ ื›ืขืช ืžืฉืจื˜ื˜ ืืช ื”ืจื‘ื™ืข ื”ืจืืฉื•ืŸ, ืื‘ืœ ืืชื” ื™ื›ื•ืœ
  • 6:56 - 6:59
    ืœื”ืžืฉื™ืš ืœื›ื•ื•ืŸ ื”ืฉืœื™ืœื™ ื‘ื›ืœ ืื—ื“ ืžื”ืฆื™ืจื™ื, ืื ืืช ืจื•ืฆื”.
  • 6:59 - 7:01
    ืื– ืžื” ื”ื“ื‘ืจ ื”ื–ื” ืขื•ืฉื”?
  • 7:01 - 7:02
    ื˜ื•ื‘, ื–ื” ืœืžืขืฉื” ืื•ืžืจ, ื”ืกืชื›ืœ.
  • 7:02 - 7:07
    ืืชื” ื ื•ืชืŸ ืœื™ X ื›ืœืฉื”ื•, ื• Y ื›ืœืฉื”ื•, ื‘ืชื•ืš ืžืจื—ื‘ X-Y,
  • 7:07 - 7:10
    ื”ื ื”ืจื™ ื™ื”ื™ื• ืžืกืคืจื™ื ื›ืœืฉื”ื, ื ื›ื•ืŸ?
  • 7:10 - 7:13
    ื›ืืฉืจ ืืชื” ืฉื X ื• Y ื›ืืŸ, ืืชื” ื”ื•ืœืš ืœืงื‘ืœ ืขืจืš ื›ืœืฉื”ื•. ื›ืืฉืจ ืืชื”
  • 7:13 - 7:14
    ืฉื X ื• Y ื›ืืŸ, ืืชื” ื”ื•ืœืš ืœืงื‘ืœ ืขืจืš ืื—ืจ.
  • 7:14 - 7:17
    ืื– ืืชื” ื”ื•ืœืš ืœืงื‘ืœ ืื™ื–ืฉื”ื• ืฆื™ืจื•ืฃ ืฉืœ ื”ืจื›ื™ื‘ื™ื ื”ื•ืงื˜ื•ืจื™ื ืฉืœ i
  • 7:17 - 7:18
    ื•ืฉืœ j.
  • 7:18 - 7:20
    ืื– ืืชื” ื”ื•ืœืš ืœืงื‘ืœ ื›ืžื” ื•ื•ืงื˜ื•ืจื™ื.
  • 7:20 - 7:23
    ืื– ืžื” ืฉื–ื” ืขื•ืฉื”, ื–ื” ืžื’ื“ื™ืจ ื•ื•ืงื˜ื•ืจ ืืฉืจ ืžืฉื•ื™ืš
  • 7:23 - 7:25
    ืœื›ืœ ื ืงื•ื“ื” ื‘ืžืจื—ื‘ X-Y.
  • 7:25 - 7:29
    ืื– ืืชื” ื™ื›ื•ืœ ืœื”ื’ื™ื“, ืื ืื ื™ ืœื•ืงื— ืืช ื”ื ืงื•ื“ื” ื”ื–ื• ื‘ืžืจื—ื‘ X-Y,
  • 7:29 - 7:32
    ื•ืื ื™ ืžื•ืชื— ืืช ื–ื” ืœื›ืืŸ, ืื ื™ ืืงื‘ืœ ื›ืคื•ืœื” ืฉืœ ื”ื•ืงื˜ื•ืจ i
  • 7:32 - 7:35
    ื•ืขื•ื“ ืžืกืคืจ ืคืขืžื™ื j, ื•ื›ืฉืืชื” ืžื—ื‘ืจ ื‘ื™ืŸ ื”ืฉื ื™ื™ื ื”ืœืœื•, ืื•ืœื™ ืื ื™ ืืงื‘ืœ
  • 7:35 - 7:37
    ื•ืงื˜ื•ืจ ืฉื ืจืื” ืžืฉื”ื• ื›ื–ื”.
  • 7:37 - 7:38
    ื•ืืชื” ื™ื›ื•ืœ ืœืขืฉื•ืช ืืช ื–ื” ืœื’ื‘ื™ ื›ืœ ื ืงื•ื“ื”.
  • 7:38 - 7:39
    ืื ื™ ืคืฉื•ื˜ ืœื•ืงื— ื“ื’ื™ืžื•ืช ืืงืจืื™ื•ืช.
  • 7:39 - 7:41
    ืื•ืœื™ ื›ืฉืื ื™ ืžื’ื™ืข ืœื›ืืŸ, ื”ื•ื•ืงื˜ื•ืจ ื ืจืื”
  • 7:41 - 7:42
    ืžืฉื”ื• ื›ื–ื”.
  • 7:42 - 7:45
    ืื•ืœื™ ื›ืฉืื ื™ ื”ื•ืœืš ืœื›ืืŸ, ื”ื•ื•ืงื˜ื•ืจ ื ืจืื” ื›ืš.
  • 7:45 - 7:48
    ืื•ืœื™ ื›ืฉืื ื™ ื”ื•ืœืš ืœื›ืืŸ, ื”ื•ื•ืงื˜ื•ืจ ื ืจืื” ืฉื•ื ื”.
  • 7:48 - 7:50
    ื•ืื•ืœื™ ื›ืืฉืจ ืื ื™ ืขื•ืœื” ื›ืืŸ ืœืžืขืœื”, ื”ื•ืงื˜ื•ืจ ื”ื•ืœืš ื›ืš.
  • 7:50 - 7:52
    ืื ื™ ืจืง ื‘ื•ื—ืจ ื ืงื•ื“ื•ืช ื‘ืื•ืคืŸ ืืงืจืื™.
  • 7:52 - 7:57
    ื–ื” ืžื’ื“ื™ืจ ื•ืงื˜ื•ืจ ื‘ื›ืœ ื”ืงื•ืจื“ื™ื ื˜ื•ืช ืฉืœ x,y ืฉื‘ื”ืŸ
  • 7:57 - 8:01
    ื”ืคื•ื ืงืฆื™ื•ืช ื”ืกืงืœืจื™ื•ืช ืžื•ื’ื“ืจื•ืช ื‘ืฆื•ืจื” ื ื›ื•ื ื”.
  • 8:01 - 8:02
    ื•ื–ื• ื”ืกื™ื‘ื” ืฉื–ื” ื ืงืจื ืฉื“ื” ื•ื•ืงื˜ื•ืจื™.
  • 8:02 - 8:07
    ื–ื” ืžื’ื“ื™ืจ ืžื” ื”ืคื•ื˜ื ืฆื™ืืœ, ื•ืื•ืœื™ ืžื”ื• ื”ื›ื•ื— ื”ื–ื”,
  • 8:07 - 8:11
    ืื• ื›ืœ ืกื•ื’ ืื—ืจ ืฉืœ ื›ื•ื—, ื‘ื›ืœ ื ืงื•ื“ื”.
  • 8:11 - 8:14
    ื‘ื›ืœ ื ืงื•ื“ื”, ืื ื™ืฉ ืœืš ืžืฉื”ื• ืฉื.
  • 8:14 - 8:16
    ื–ื” ืœืžืขืฉื” ื”ืคื•ื ืงืฆื™ื”.
  • 8:16 - 8:18
    ื•ืื ื™ ืืžืฉื™ืš ืœืขืฉื•ืช ืืช ื–ื” ืœืขื•ืœื,
  • 8:18 - 8:19
    ื•ืืžืœื ืืช ื›ืœ ื”ืคืขืจื™ื.
  • 8:19 - 8:20
    ืื‘ืœ ืื ื™ ื—ื•ืฉื‘ ืฉื”ื‘ื ืชื ืืช ื”ืจืขื™ื•ืŸ.
  • 8:20 - 8:25
    ื–ื” ืžื›ื™ืœ ื›ืœ ื•ื•ืงื˜ื•ืจ ืืฉืจ ื›ืœ ื”ื ืงื•ื“ื•ืช ืฉืœื• ื ืžืฆืื•ืช ื‘ืžืจื—ื‘ X-Y.
  • 8:25 - 8:29
    ื›ืขืช, ื–ื” ื ืงืจื ืฉื“ื” ื•ื•ืงื˜ื•ืจื™, ืื– ืกื‘ื™ืจ
  • 8:29 - 8:31
    ืฉื”ื’ื™ื•ื ื™ ืฉื–ื” ื™ืฉืžืฉ ื›ื“ื™ ืœืชืืจ
  • 8:31 - 8:32
    ื›ืœ ืกื•ื’ ืฉืœ ืฉื“ื”.
  • 8:32 - 8:33
    ื–ื” ื™ื›ื•ืœ ืœื”ื™ื•ืช ืฉื“ื” ื›ื‘ื™ื“ื”.
  • 8:33 - 8:37
    ื–ื” ื™ื›ื•ืœ ืœื”ื™ื•ืช ืฉื“ื” ื—ืฉืžืœื™, ื•ื–ื” ื™ื›ื•ืœ ืœื”ื™ื•ืช ืฉื“ื” ืžื’ื ื˜ื™.
  • 8:37 - 8:40
    ื•ื–ื” ื—ื™ื•ื ื™ ืœืกืคืจ ืœืš ื›ืžื” ื›ื•ื—
  • 8:40 - 8:43
    ื™ื•ืฉืงืข ื‘ืื™ื–ืฉื”ื• ื’ื•ืฃ ื‘ืฉื“ื” ื”ื–ื”.
  • 8:43 - 8:45
    ื–ื” ื‘ื“ื™ื•ืง ืžื” ืฉื–ื” ื™ืชืืจ.
  • 8:45 - 8:49
    ื›ืขืช, ื‘ื•ืื• ื ื’ื™ื“ ืฉื‘ืฉื“ื” ื”ื–ื”, ื™ืฉ ืœื™ ื’ื•ืฃ ืžืกื•ื™ื
  • 8:49 - 8:52
    ื”ื ืข ื‘ืžืจื—ื‘ X-Y.
  • 8:52 - 8:59
    ื‘ื•ืื• ื ื’ื™ื“ ืฉื–ื” ืžืชื—ื™ืœ ื›ืืŸ, ื•ื‘ื’ืœืœ ื›ืœ
  • 8:59 - 9:04
    ื”ื›ื•ื—ื•ืช ื”ืžืฉื•ื’ืขื™ื ื”ืคื•ืขืœื™ื ืขืœ ื”ื’ื•ืฃ, ื•ืื•ืœื™ ื”ื’ื•ืฃ ื’ื ื ืžืฆื ืขืœ ืื™ื–ื” ืžืกืœื•ืœ
  • 9:04 - 9:07
    ืื• ืžืฉื”ื•, ืื– ื–ื” ืœื ืชืžื™ื“ ื™ื ื•ืข ื‘ื“ื™ื•ืง
  • 9:07 - 9:09
    ื‘ื›ื™ื•ื•ืŸ ืฉื”ืฉื“ื” ืžื ืกื” ืœื”ื–ื™ื– ืื•ืชื• ืืœื™ื•.
  • 9:09 - 9:14
    ื‘ื•ืื• ื ื’ื™ื“ ืฉื–ื” ื ืข ื‘ืžืกืœื•ืœ ืฉื–ื– ื›ืžื• ืžืฉื”ื• ื›ื–ื”.
  • 9:14 - 9:18
    ื•ื‘ื•ืื• ื ื’ื™ื“ ืฉื”ืžืกืœื•ืœ ื”ื–ื”, ืื• ื”ืขืงื•ืžื” ื”ื–ื•, ืžื•ื’ื“ืจืช
  • 9:18 - 9:22
    ืขืœ ื™ื“ื™ ืคื•ื ืงืฆื™ื” ื•ืงื˜ื•ืจื™ืช.
  • 9:22 - 9:25
    ืื– ื‘ื•ืื• ื ื’ื™ื“ ืฉืžื” ืฉืžื•ื’ื“ืจ ืขืœ ื™ื“ื™ r ืื• t, ืืฉืจ
  • 9:25 - 9:34
    ื–ื” ืื•ืžืจ x ืฉืœ t ื›ืคื•ืœ i ื•ืขื•ื“ y ืฉืœ t ื›ืคื•ืœ ื’ื•ืจื ื”ื™ื—ื™ื“ื” j.
  • 9:34 - 9:35
    ื–ื” r ืื• t ืžืžืฉ ื›ืืŸ.
  • 9:35 - 9:38
    ืื•ืงื™, ืขืœ ืžื ืช ืฉื–ื• ืชื”ื™ื” ื“ืจืš ืกื•ืคื™ืช
  • 9:38 - 9:42
    ื ื’ื“ื™ืจ ืืช t ื›ืš ืฉื™ื”ื™ื” ื’ื“ื•ืœ ืื• ืฉื•ื•ื” ืœ a, ื•ืงื˜ืŸ
  • 9:42 - 9:46
    ืื• ืฉื•ื•ื” ืœ b.
  • 9:46 - 9:48
    ื–ื” ื”ืžืกืœื•ืœ ืฉื”ื’ื•ืฃ ื ื•ื˜ื” ืœืงื—ืช,
  • 9:48 - 9:50
    ื‘ืขืงื‘ื•ืช ื›ืœ ื”ื›ื•ื—ื•ืช ื”ืžื˜ื•ืจืคื™ื ื”ืœืœื• ื”ืคื•ืขืœื™ื ืขืœื™ื•.
  • 9:50 - 9:54
    ืื– ื›ืืฉืจ ื”ื’ื•ืฃ ื ืžืฆื ื›ืืŸ, ืื– ื”ืฉื“ื” ื”ื•ื•ืงื˜ื•ืจื™
  • 9:54 - 9:57
    ืคื•ืขืœ ืขืœื™ื•, ื•ืื•ืœื™ ืžืคืขื™ืœ ืขืœื™ื• ื›ื•ื— ื›ื–ื”.
  • 9:57 - 10:00
    ืื‘ืœ ื›ื™ื•ื•ืŸ ืฉื”ื’ื•ืฃ ื ืžืฆื ืขืœ ืžืกืœื•ืœ ื›ืœืฉื”ื•, ื”ื•ื ื–ื–
  • 10:00 - 10:00
    ื‘ื›ื™ื•ื•ืŸ ื”ื–ื”.
  • 10:00 - 10:04
    ื•ืื– ื›ืืฉืจ ื”ื•ื ื ืžืฆื ื›ืืŸ, ืื•ืœื™ ื”ืฉื“ื” ื”ื•ื•ืงื˜ื•ืจื™ ื”ื•ื ื›ื–ื”,
  • 10:04 - 10:06
    ืื‘ืœ ื”ื•ื ื–ื– ื‘ื›ื™ื•ื•ืŸ ื”ื”ื•ื, ื‘ื’ืœืœ ืฉื”ื•ื ืขืœ
  • 10:06 - 10:07
    ืื™ื–ืฉื”ื• ืกื•ื’ ืฉืœ ืžืกืœื•ืœ.
  • 10:07 - 10:10
    ื›ืขืช, ื›ืœ ืžื” ืฉืขืฉื™ืชื™ ื‘ืกืจื˜ื•ืŸ ื”ื–ื” ื”ื•ื ืœืขื ื•ืช
  • 10:10 - 10:11
    ืขืœ ืฉืืœื” ืขืงืจื•ื ื™ืช.
  • 10:11 - 10:14
    ืžื” ื”ื™ื™ืชื” ื”ืขื‘ื•ื“ื” ืฉื ืขืฉืชื” ืขืœ ื”ื’ื•ืฃ ืขืœ ื™ื“ื™ ื”ืฉื“ื”?
  • 10:14 - 10:25
  • 10:25 - 10:29
    ื‘ืฉื‘ื™ืœ ืœืขื ื•ืช ืขืœ ื”ืฉืืœื” ื”ื–ื•, ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœื”ืชืžืงื“ ืžืขื˜.
  • 10:29 - 10:31
    ืื ื™ ื”ื•ืœืš ืœื”ืชืžืงื“ ืจืง ืขืœ ื—ืœืง ืงื˜ืŸ
  • 10:31 - 10:35
    ืฉืœ ื”ื“ืจืš ืฉืœื ื•.
  • 10:35 - 10:38
    ื•ื‘ื•ืื• ื ื ืกื” ืœื’ืœื•ืช ืžื” ื”ืขื‘ื•ื“ื” ืฉื ืขืฉืชื”
  • 10:38 - 10:40
    ื‘ื—ืœืง ืงื˜ืŸ ืžืื•ื“ ืžื”ืžืกืœื•ืœ ืฉืœื ื•, ื‘ื’ืœืœ ืฉื”ื•ื ืžืฉืชื ื” ื›ืœ ื”ื–ืžืŸ.
  • 10:40 - 10:42
    ื”ืฉื“ื” ืžืฉื ื” ื›ื™ื•ื•ืŸ.
  • 10:42 - 10:44
    ื”ื’ื•ืฃ ืฉืœื ื• ืžืฉื ื” ื›ื™ื•ื•ืŸ.
  • 10:44 - 10:48
    ืื– ื‘ื•ืื• ื ื’ื™ื“ ืฉื›ืฉืื ื™ ื›ืืŸ, ื•ืื ื™ ื–ื–
  • 10:48 - 10:50
    ื‘ื—ืœืง ืงื˜ืŸ ืžืื•ื“ ืžื”ื“ืจืš ืฉืœื™,
  • 10:50 - 10:56
    ืื– ื‘ื•ืื• ื ื’ื™ื“ ืฉืื ื™ ื–ื–, ื‘ืžื™ื“ื” ืงื˜ื ื” ืžืื•ื“,
  • 10:56 - 10:58
    ืžืžืฉ ื“ืœืชื r ืงื˜ืŸ, ื ื›ื•ืŸ?
  • 10:58 - 11:01
    ื™ืฉ ืœื™ ื”ืคืจืฉ ื›ืœืฉื”ื•, ืฉื”ื• ื”ืคืจืฉ ื•ืงื˜ื•ืจื™,
  • 11:01 - 11:03
    ื‘ืžืจื—ืง ืงื˜ืŸ ืžืื•ื“.
  • 11:03 - 11:07
    ื•ื‘ื•ืื• ื ื’ื™ื“ ืฉื‘ืžื”ืœืš ื–ื”, ื”ืฉื“ื” ื”ื•ื•ืงื˜ื•ืจื™
  • 11:07 - 11:09
    ืคื•ืขืœ ื‘ื›ืœ ื”ืื–ื•ืจ ื”ื›ืœืœื™ ื”ื–ื”, ื‘ื•ืื• ื ื’ื™ื“ ืฉื”ื•ื ื ืจืื”
  • 11:09 - 11:10
    ื›ืžื• ืžืฉื”ื• ื›ื–ื”.
  • 11:10 - 11:13
    ื–ื” ืžืกืคืง ื›ื•ื— ืฉื ืจืื” ื›ืžื• ืžืฉื”ื• ื›ื–ื”.
  • 11:13 - 11:17
    ืื– ื–ื”ื• ืฉื“ื” ื•ื•ืงื˜ื•ืจื™ ื‘ืื–ื•ืจ ื”ื”ื•ื, ืื• ื”ื›ื•ื—
  • 11:17 - 11:19
    ื”ืžื›ื•ื•ืŸ ืขืœ ื”ื’ื•ืฃ ื”ื–ื” ื›ืืฉืจ ื”ื•ื ื‘ื ืงื•ื“ื” ื–ื•.
  • 11:19 - 11:19
    ื ื›ื•ืŸ?
  • 11:19 - 11:22
    ื–ื” ื–ืžืŸ ืงืฆืจ ืžืื•ื“ ืฉืœ ืชื ื•ืขื” ื‘ืžืจื—ื‘.
  • 11:22 - 11:24
    ืืชื” ื™ื›ื•ืœ ืœื”ื’ื™ื“ "ื˜ื•ื‘, ื‘ื ืงื•ื“ื” ื”ืกืคืฆื™ืคื™ืช ื”ื–ื•, ื™ืฉ
  • 11:24 - 11:27
    ืœื ื• ืืช ื”ื›ื•ื— ื”ืงื‘ื•ืข ื”ื–ื”".
  • 11:27 - 11:30
    ืžื” ื”ื™ื™ืชื” ื”ืขื‘ื•ื“ื” ืฉื”ื•ืฉืงืขื” ื‘ืคืจืง ื”ื–ืžืŸ ื”ืงืฆืจ ื”ื–ื”?
  • 11:30 - 11:32
    ืืชื” ื™ื›ื•ืœ ืœื”ื’ื™ื“, ืžื” ื”ืจื•ื•ื— ืžื”ืขื‘ื•ื“ื” ื‘ื–ืžืŸ ื–ื”?
  • 11:32 - 11:36
    ื›ืœื•ืžืจ, ื ื™ืชืŸ ืœื”ื’ื™ื“, ื“ืœืชื ืฉืœ ื”ืขื‘ื•ื“ื”, ืื• ื”ื”ืคืจืฉ ืฉืœ ื”ืขื‘ื•ื“ื”.
  • 11:36 - 11:39
    ื˜ื•ื‘, ื‘ื“ื™ื•ืง ืขืœ ืคื™ ืื•ืชื• ื”ื”ื’ื™ื•ืŸ ืฉืขืœ ืคื™ื• ืคืชืจื ื• ืืช ื”ื‘ืขื™ื” ื”ืคืฉื•ื˜ื”,
  • 11:39 - 11:44
    ื–ื”ื• ื”ื’ื•ื“ืœ ืฉืœ ื”ื›ื•ื— ื‘ื›ื™ื•ื•ืŸ ืฉืœ ื”ืชื ื•ืขื”
  • 11:44 - 11:49
    ื›ืคื•ืœ ื”ื’ื•ื“ืœ ืฉืœ ื”ืžืจื—ืง.
  • 11:49 - 11:53
    ื•ืื ื—ื ื• ื™ื•ื“ืขื™ื ืžื” ื–ื”, ืœืคื™ ื”ื“ื•ื’ืžื ื”ื "ืœ.
  • 11:53 - 11:55
    ื–ื•ื”ื™ ื”ืžื›ืคืœื” ื”ืกืงืœืจื™ืช.
  • 11:55 - 11:58
    ื–ื•ื”ื™ ื”ืžื›ืคืœื” ื”ืกืงืœืจื™ืช ืฉืœ ื”ื›ื•ื— ื•ื”ืžืจื—ืง
  • 11:58 - 11:59
    ื”ืžืžืฉ ืงื˜ืŸ ืฉืœื ื•.
  • 11:59 - 12:08
    ืื– ื–ื” ืฉื•ื•ื” ืœืžื›ืคืœื” ื”ืกืงืœืจื™ืช ืฉืœ ื”ื›ื•ื— ื•ืฉืœ
  • 12:08 - 12:10
    ื”ืคืจืฉ ื”ืžืจื—ืง.
  • 12:10 - 12:13
    ื›ืขืช, ืจืง ื‘ื–ื›ื•ืช ืฉืื ื• ืขื•ืฉื™ื ื–ืืช, ืื ื—ื ื• ืžื’ืœื™ื
  • 12:13 - 12:16
    ืžื”ื™ ื”ืขื‘ื•ื“ื”, ืื•ืœื™ ืจืง ืขื‘ื•ืจ ื”ืคืจืฉ ืžืจื—ืง ืžืื•ื“ ืžืื•ื“ ืงื˜ืŸ, ืื‘ืœ
  • 12:16 - 12:19
    ืžื” ืฉืื ื• ืจื•ืฆื™ื ืœืขืฉื•ืช ื–ื” ืœืžืฆื•ื ืืช ื”ืกื›ื•ื ืฉืœ ื›ืœ ื”ืขื‘ื•ื“ื•ืช.
  • 12:19 - 12:22
    ืื ื—ื ื• ื•ืฆื™ื ืœืกื›ื ืืช ื›ืœ ื”ืคืจืฉื™ ื”ืžืจื—ืงื™ื ื”ืงื˜ื ื™ื ืขืœ ืžื ืช ืœื’ืœื•ืช ืืช ื”ืกื›ื•ื ื”ื›ื•ืœืœ,
  • 12:22 - 12:25
    ื›ืœ ื”ื›ื•ื—ื•ืช ื›ืคื•ืœ (ื‘ืžื›ืคืœื” ืกืงืœืจื™ืช) ื”ืคืจืฉื™ ื”ืžืจื—ืงื™ื, ืขืœ ืžื ืช ืœื’ืœื•ืช ืืช ื”ืขื‘ื•ื“ื” ื”ื›ื•ืœืœืช ืฉื”ื•ืฉืงืขื” ื›ืืŸ.
  • 12:25 - 12:28
    ื•ื–ื” ื”ื—ืœืง ืฉื‘ื• ืžื’ื™ืข ื”ืื™ื ื˜ื’ืจืœ.
  • 12:28 - 12:33
    ืื ื—ื ื• ื ื—ืฉื‘ ืื ื˜ื’ืจืœ - ืื ื™ ืžืชื›ื•ื•ืŸ ืฉืืชื” ื™ื›ื•ืœ
  • 12:33 - 12:34
    ืœื—ืฉื•ื‘ ืขืœ ื–ื” ื‘ืฉืชื™ ื“ืจื›ื™ื.
  • 12:34 - 12:37
    ืืชื” ื™ื›ื•ืœ ืœืจืฉื•ื ืคืฉื•ื˜ d ื‘ืžื›ืคืœื” ืกืงืœืจื™ืช ืฉืœ w, ืื‘ืœ ื ื™ืชืŸ ื’ื ืœื”ื’ื™ื“ ืฉืื ื—ื ื•
  • 12:37 - 12:43
    ื ืขืฉื” ืื ื˜ื’ืจืœ ืฉืœ ื”ืขืงื•ืžื” ื”ื–ื• c, ื›ืœื•ืžืจ, ืฉ c,
  • 12:43 - 12:46
    ืื• r, ืื™ืš ืฉืชืจืฆื” ืœืงืจื•ื ืœื–ื”, ืฉืœ ื“ืœืชื w.
  • 12:46 - 12:48
    ื–ื” ื™ื™ืชืŸ ืœื ื• ืืช ื”ืขื‘ื•ื“ื” ื”ื›ื•ืœืœืช.
  • 12:48 - 12:50
    ืื– ื‘ื•ืื• ื ื’ื™ื“ ืฉื”ืขื‘ื•ื“ื”, ืฉื•ื•ื” ืœื–ื”.
  • 12:50 - 12:54
    ืื• ืฉืื ื—ื ื• ื’ื ื™ื›ื•ืœื™ื ืœืจืฉื•ื ื–ืืช ืขืœ ื”ืื™ื ื˜ื’ืจืœ, ืขืœ ืื•ืชื”
  • 12:54 - 13:00
    ื”ืขืงื•ืžื” ืฉืœ f ืฉืœ f ื›ืคื•ืœ ื“ืœืชื r.
  • 13:00 - 13:04
    ื•ื›ื ืจืื” ืฉื–ื” ื™ื™ืจืื” ื‘ืืžืช ื›ืžื•, ืืชื” ื™ื•ื“ืข,
  • 13:04 - 13:05
    ื‘ืื•ืคืŸ ืžืื•ื“ ืžื•ืคืฉื˜.
  • 13:05 - 13:09
    ืื™ืš ืื ื—ื ื• ืœืžืขืฉื” ืžื—ืฉื‘ื™ื ืžืฉื”ื• ื›ื–ื”?
  • 13:09 - 13:13
    ื‘ืžื™ื•ื—ื“ ื‘ื’ืœืœ ืฉื™ืฉ ืœื ื• ืืช ื›ืœ ื”ืคืจืžื˜ืžืจื™ื
  • 13:13 - 13:14
    ื‘ืžื•ื ื—ื™ื ืฉืœ t.
  • 13:14 - 13:16
    ืื™ืš ืื ื—ื ื• ืžืงื‘ืœื™ื ืืช ื–ื” ื‘ืžื•ื ื—ื™ื ืฉืœ t?
  • 13:16 - 13:20
    ื•ืื ืืชื” ื—ื•ืฉื‘ ืขืœ ื–ื” ืœืจื’ืข, ืžื” ื–ื” ื‘ื›ืœืœ f ื›ืคื•ืœ (ืกืงืœืจื™) r?
  • 13:20 - 13:21
    ืื• ืžื” ื–ื” f ื›ืคื•ืœ ื“ืœืชื r?
  • 13:21 - 13:23
    ื˜ื•ื‘, ืœืžืขืฉื”, ื‘ืฉื‘ื™ืœ ืœืขื ื•ืช ืขืœ ื–ื”, ื‘ื•ืื• ื ื–ื›ื•ืจ
  • 13:23 - 13:26
    ืื™ืš ื ืจืื” ื“ืœืชื r.
  • 13:26 - 13:36
    ืื ืืชื” ื–ื•ื›ืจ, ื“ืœืชื r ื—ืœืงื™ ื“ืœืชื t ืฉื•ื•ื™ื ืœx ื˜ืื’ ืฉืœ t, ืื ื™ ืจื•ืฉื ืืช ื–ื”,
  • 13:36 - 13:39
    ื•ื™ื›ื•ืœืชื™ ื’ื ืœืจืฉื•ื ื“ืœืชื x ื—ืœืงื™ ื“ืœืชื t ืื ื”ื™ื™ืชื™ ืจื•ืฆื”, ื›ืคื•ืœ
  • 13:39 - 13:45
    ื”ืจื›ื™ื‘ ื”ื•ืงื˜ื•ืจื™ i, ื•ืขื•ื“ y ื˜ืื’ ืฉืœ t ื›ืคื•ืœ ื”ืจื›ื™ื‘ ื”ื•ื•ืงื˜ื•ืจื™ j.
  • 13:45 - 13:49
    ื•ืื ืื ื—ื ื• ืจืง ืจื•ืฆื™ื ืืช ื“ืœืชื r, ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœื”ื›ืคื™ืœ ืืช ืฉื ื™ ื”ืฆื“ื“ื™ื, ืื
  • 13:49 - 13:52
    ื ื”ื™ื” ืงืฆืช ืคื—ื•ืช ืงืคื“ื ื™ื ืขื
  • 13:52 - 13:53
    ื”ืžืฉื•ื•ืื•ืช, ืœื ื™ื•ืชืจ ืžื“ื™ ืžื“ื•ื™ืงื™ื.
  • 13:53 - 13:58
    ืื ื—ื ื• ื ืงื‘ืœ ืฉื“ืœืชื r ืฉื•ื•ื” ืœx ื˜ืื’ ืฉืœ t, ื›ืคื•ืœ ื“ืœืชื t, ื›ืคื•ืœ ื”ืจื›ื™ื‘ ื”ื•ื•ืงื˜ื•ืจื™
  • 13:58 - 14:05
    i, ื•ืขื•ื“ y ื˜ืื’ ืฉืœ t, ื›ืคื•ืœ ื”ื”ืคืจืฉ ืฉืœ ื“ืœืชื t
  • 14:05 - 14:07
    ื›ืคื•ืœ ื”ืจื›ื™ื‘ ื”ื•ื•ืงื˜ื•ืจื™ j.
  • 14:07 - 14:09
    ืื– ื–ื” ืžืžืฉ ื›ืืŸ.
  • 14:09 - 14:12
  • 14:12 - 14:16
    ื•ืชื–ื›ื•ืจ ืžื” ื”ื™ื” ื”ืฉื“ื” ื”ื•ื•ืงื˜ื•ืจื™ ืฉืœื ื•.
  • 14:16 - 14:17
    ื–ื” ื”ื™ื” ื”ื“ื‘ืจ ื”ื–ื” ื›ืืŸ ืœืžืขืœื”.
  • 14:17 - 14:20
    ืชืŸ ืœื™ ืœื”ืขืชื™ืง ื•ืœื”ื“ื‘ื™ืง ืืช ื–ื”.
  • 14:20 - 14:21
    ื•ืื ื—ื ื• ื ืจืื” ืฉื”ืžื›ืคืœื” ื”ื•ื•ืงื˜ื•ืจื™ืช
  • 14:21 - 14:23
    ื”ื™ื ืœื ื›ืœ ื›ืš ืžื•ืจื›ื‘ืช.
  • 14:23 - 14:27
    ืื– ืื ื™ ืžืขืชื™ืง, ื•ืžื“ื‘ื™ืง ืืช ื–ื” ืžืžืฉ ื›ืืŸ.
  • 14:27 - 14:31
  • 14:31 - 14:34
    ืื– ืื™ืš ื”ื•ืœืš ืœื”ื™ืจืื•ืช ื”ืื ื˜ื’ืจืœ?
  • 14:34 - 14:38
    ื”ืื™ื ื’ืจืœ ื”ื–ื” ืžืžืฉ ื›ืืŸ, ื ื•ืชืŸ ืืช ื”ืขื‘ื•ื“ื” ื”ื›ื•ืœืœืช ืฉื”ื•ืฉืงืขื”
  • 14:38 - 14:41
    ืขืœ ื™ื“ื™ ื”ืฉื“ื” ืขืœ ื”ื’ื•ืฃ, ื‘ื–ืžืŸ ืฉื”ื•ื ื ืข ื‘ืžืกืœื•ืœ.
  • 14:41 - 14:44
    ื–ื” ื”ื‘ืกื™ืก, ืคื—ื•ืช ืื• ื™ื•ืชืจ, ืœื›ืœ ื“ื‘ืจ ืžื•ืจื›ื‘ ื•ืจืฆื™ื ื™ ื‘ืคื™ื–ื™ืงื”
  • 14:44 - 14:47
    ืฉืื•ืœื™ ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ ืชืžืฆื ืืช ืขืฆืžืš ืขื•ืกืง ื‘ื•.
  • 14:47 - 14:48
    ื•ืื– ืชื•ื›ืœ ืœื”ื’ื™ื“ ืฉื–ื” ืžื•ื‘ืŸ.
  • 14:48 - 14:52
    ื–ื” ื”ื•ืœืš ืœื”ื™ื•ืช ืื™ื ื˜ื’ืจืœ, ื‘ื•ืื• ืคืฉื•ื˜ ื ื’ื™ื“ ืฉื–ื” ื”ื”ืคืจืฉ ืž t ืฉื•ื•ื”
  • 14:52 - 14:55
    ืœ a , ืœ t ืฉื•ื•ื” ืœ b.
  • 14:55 - 14:58
    ื ื›ื•ืŸ? a ื–ื” ื”ืžื™ืงื•ื ื”ื”ืชื—ืœืชื™, t ืฉื•ื•ื” ืœ a ืขื“ ืฉ t ืฉื•ื•ื” ืœ b (ื”ืžื™ืงื•ื ื”ืกื•ืคื™).
  • 14:58 - 15:00
    ืœ a ืœ t ืฉื•ื•ื” ืœ b.
  • 15:00 - 15:02
    ืืชื” ื™ื›ื•ืœ ืœื“ืžื™ื™ืŸ ืืช ื–ื” ื›ื“ื‘ืจ ืฉืชืœื•ื™ ื‘ื–ืžืŸ, ื›ืžื• ื’ื•ืฃ
  • 15:02 - 15:04
    ืฉื–ื–, ื›ื›ืœ ืฉืขื•ื‘ืจ ื”ื–ืžืŸ.
  • 15:04 - 15:07
    ื•ืื– ืžื” ื–ื” f ื›ืคื•ืœ ื“ืœืชื r?
  • 15:07 - 15:11
    ื˜ื•ื‘, ืื ืืชื” ื–ื•ื›ืจ ืžื” ืื•ืžืจืช ื”ืžื›ืคืœื” ื”ืกืงืœืจื™ืช, ืืชื”
  • 15:11 - 15:15
    ื™ื›ื•ืœ ืคืฉื•ื˜ ืœืงื—ืช ืืช ื”ืชื•ืฆืื” ืฉืœ
  • 15:15 - 15:18
    ื”ืจื›ื™ื‘ื™ื ื”ืžืชืื™ืžื™ื ื‘ื•ื•ืงื˜ื•ืจ ืฉืœืš, ื•ืœื—ื‘ืจ ืื•ืชื.
  • 15:18 - 15:20
    ืื– ื–ื” ื”ื•ืœืš ืœื”ื™ื•ืช ืื™ื ื’ืจืœ ืžt ืฉืฉื•ื•ื” ืœ a ืขื“ ืœ t
  • 15:20 - 15:27
    ืฉืฉื•ื•ื” ืœ b, ืฉืœ p ืฉืœ p ืฉืœ x, ื‘ืืžืช, ื‘ืžืงื•ื ืœืจืฉื•ื x,
  • 15:27 - 15:31
    y, ื–ื” x ืฉืœ t , ื ื›ื•ืŸ? x ื›ืžื• a ื›ืคื•ื ืงืฆื™ื” ืฉืœ t, ื• y ื›ืžื•
  • 15:31 - 15:32
    a ืคื•ื ืงืฆื™ื” ืฉืœ t.
  • 15:32 - 15:34
  • 15:34 - 15:38
  • 15:38 - 15:39
  • 15:39 - 15:51
  • 15:51 - 15:52
  • 15:52 - 15:56
  • 15:56 - 15:58
  • 15:58 - 15:59
  • 15:59 - 16:10
  • 16:10 - 16:12
  • 16:12 - 16:16
  • 16:16 - 16:17
  • 16:17 - 16:17
  • 16:17 - 16:19
  • 16:19 - 16:23
  • 16:23 - 16:25
  • 16:25 - 16:27
  • 16:27 - 16:30
  • 16:30 - 16:32
  • 16:32 - 16:35
  • 16:35 - 16:38
  • 16:38 - 16:43
  • 16:43 - 16:46
  • 16:46 - 16:46
Title:
Line Integrals and Vector Fields
Description:
more » « less
Video Language:
English
Duration:
16:46
ื ื’ื” ืžื•ื“ืจื™ืง edited Hebrew subtitles for Line Integrals and Vector Fields
ื ื’ื” ืžื•ื“ืจื™ืง edited Hebrew subtitles for Line Integrals and Vector Fields
ื ื’ื” ืžื•ื“ืจื™ืง edited Hebrew subtitles for Line Integrals and Vector Fields
ื ื’ื” ืžื•ื“ืจื™ืง edited Hebrew subtitles for Line Integrals and Vector Fields
ื ื’ื” ืžื•ื“ืจื™ืง edited Hebrew subtitles for Line Integrals and Vector Fields
ื ื’ื” ืžื•ื“ืจื™ืง edited Hebrew subtitles for Line Integrals and Vector Fields
ื ื’ื” ืžื•ื“ืจื™ืง edited Hebrew subtitles for Line Integrals and Vector Fields
ื ื’ื” ืžื•ื“ืจื™ืง edited Hebrew subtitles for Line Integrals and Vector Fields
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  • Revision 21 Edited
    ื ื’ื” ืžื•ื“ืจื™ืง
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