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Differential Forms - Cartan

  1. Nov 15, 2006 #1

    acm

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    Hello,

    I'm interested in starting differential forms, Is this book any good? What audience is it intended for? What prerequisites (E.G. Linear Algebra, Calculus(At what level), etc.) would one need to fully appriciate the scope and depth of information presented in this book?

    Thanks for your time.
     
  2. jcsd
  3. Nov 15, 2006 #2

    mathwonk

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    thats like asking if the bible is useful for religious study. just read it, and then you will be teaching us.

    these questions are like people at the beach marching up and down the sand asking if the water is wet. just get in for christ sake.

    and ona more helpful note, if you have difficulties ask us, we will help.
     
    Last edited: Nov 15, 2006
  4. Nov 29, 2006 #3

    Chris Hillman

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    Hi, acm,

    I agree with mathwonk--- if you didn't take the point, Cartan founded the subject, but his books are often considered to be challenging to read, so if you can truly master his writings, you will probably find many eager to learn from Cartan via yourself. However, I take it that your ambitions were less lofty. Fortunately, there are many good introductory textbooks on differential forms. One of the most inexpensive is one of the few really valuable Dover books, Differential Forms with Applications to the Physical Sciences, by Harley Flanders. The much more recent (and much more expensive) book by Frankel, The Geometry of Physics, is probably more challenging, but offers more applications of differential forms (this book covers much more than just differential forms).

    Chris Hillman
     
  5. Nov 29, 2006 #4

    mathwonk

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    in was myself always mystified by diferential forms util i reqd an article by harley flanders which showed how to calculate with them.so i advise: learn to compiute with them, then what They are.

    the ARticle i read was i the little ams book on global differential geometry, edited by chern.
     
  6. Dec 1, 2006 #5

    robphy

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    acm,
    what is the first name of the author of your "Differential Forms" book?
    Is it (the father) Elie or (the son) Henri?
     
  7. Dec 1, 2006 #6

    Chris Hillman

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    Which Cartan?

    Oops, I assumed he meant the book by Elie Cartan (1869-1951), Les systèmes differentiels extérieurs et leur applications géométriques, but come to think of it, he probably meant Henri Cartan (1904-), Formes différentielles.

    For those who don't know, Elie Cartan initiated the subject of differential forms (and many other way cool things); his son Henri was also a great mathematician. Casually interested members can consult http://en.wikipedia.org/wiki/Elie_Cartan and http://en.wikipedia.org/wiki/Henri_Cartan, but as always should bear in mind the fact that Wikipedia is inherently unstable, has no effective fact checking mechanisms in place, and that misinformation and misemphasis is rampant in the physics articles, and, increasingly, in the math articles. I have not attempted to read the two articles I just cited, so I have no idea whether they are good or bad at this moment in time.
     
    Last edited: Dec 1, 2006
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