Multivariable Calculus | Curvature

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We define the notion of the curvature of a vector valued function, prove an equivalent definition, and find the curvature of a circle of radius a.

  1. Michael Penn
  2. math
  3. mathematics
  4. calculus
  5. Randolph College
  6. randolph
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Комментарии
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so many differential geometry books are painful to read; this was very clear, thank you.

programstix
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Taking multi variable calc and my book covers this with little to no explanation on what these definitions actually mean. Thank you so much - A STRUGGLING STUDENT

Spacexioms
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Nice to see you covering this, I'm taking a course on elementary differential geometry next semester so this sort of thing is useful.

technoguyx
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Thanks for the upload. It's concise and useful information, however, having notations like dT/ds or dT/dt without an explicit statement of the function composition involved ( s(t) or its inverse t(s)) makes it hard to understand; as far as I can understand it hides many of the subtleties and complexity behind this "proof" which feels far from being complete.

reup
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Maybe a cleaner blackboard would help? Thanks 😊

punditgi
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