Differential Equations | Abel's Theorem

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We present Abel's Theorem with a proof.

  1. Michael Penn
  2. math
  3. mathematics
  4. number theory
  5. abstract algebra
  6. calculus
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Комментарии
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THANK YOU！The proof is clear and easy to understand!!

henrytzuo
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Thank you for sharing these videos. They are great.

manucitomx
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At 9:22 you wrote C and said "that constant" when it should have been e^C. You could rename it to e^C=K or something, because it's just another arbitrary constant. Although that implies that K is positive, you could have written ln|W|, with the absolute value, earlier. Then it's possible for W = (Also, you kind of assumed that W was nonzero when you divided by W while separating the someone could consider the W=0 case separately if they did a more thorough proof).

When I learned about Abel's theorem in an intro to differential equations class, it seemed so arbitrary. It's nice to see a proof of it.

matthewkearney
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Hello sir, I have a doubt, can we generalize this to an nth order differential equation?? please tell me

vaibhavcm
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and that's a good place to stop for tonight

quantabot