Kelvin–Stokes theorem | Wikipedia audio article
0This is an audio version of the Wikipedia Article:\nhttps://en.wikipedia.org/wiki/Kelvin%E2%80%93Stokes_theorem\n\n\n00:02:15 1 Theorem
00:02:46 2 Proof
00:02:58 2.1 First step of the proof (defining the pullback)
00:03:51 2.2 Second step of the proof (first equation)
00:06:16 2.3 Third step of the proof (second equation)
00:12:42 2.4 Fourth step of the proof (reduction to Green's theorem)
00:23:31 3 Application for conservative vector fields and scalar potential
00:23:50 3.1 The Lamellar vector field
00:26:05 3.2 Helmholtz's theorems
00:26:31 3.3 Proof of the theorem
00:27:36 3.4 Application for conservative force
00:35:58 4 Kelvin–Stokes theorem on singular 2-cube and cube subdivisionable sphere
00:38:01 4.1 Singular 2-cube and boundary
00:38:15 4.2 Cube subdivision
00:44:55 5 Notes
\n\n\nListening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.\n\nLearning by listening is a great way to:\n- increases imagination and understanding\n- improves your listening skills\n- improves your own spoken accent\n- learn while on the move\n- reduce eye strain\n\nNow learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.\n\nListen on Google Assistant through Extra Audio:\nhttps://assistant.google.com/services/invoke/uid/0000001a130b3f91\nOther Wikipedia audio articles at:\nhttps://www.youtube.com/results?search_query=wikipedia+tts\nUpload your own Wikipedia articles through:\nhttps://github.com/nodef/wikipedia-tts\nSpeaking Rate: 0.8089621593288359\nVoice name: en-GB-Wavenet-B\n\n\n"I cannot teach anybody anything, I can only make them think."\n- Socrates\n\n\nSUMMARY\n=======\nThe Kelvin–Stokes theorem (named for Lord Kelvin and George Stokes), also known as the curl theorem, is a theorem in vector calculus on R3. Given a vector field, the theorem relates the integral of the curl of the vector field over some surface, to the line integral of the vector field around the boundary of the surface. The Kelvin–Stokes theorem is a special case of the “generalized Stokes' theorem.” In particular, a vector field on R3 can be considered as a 1-form in which case curl is the exterior derivative.
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