Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    In the notes attached I have quite a few problems with one of the proofs. In the proof of the proposition on p15,

    a) he goes from
     \{ \frac{d}{dt} [ \alpha ( x^\mu ( \lambda(t)) - x^\mu(p)) + \beta (x^\mu(\kapa(t))-x^\mu(p)) + x^\mu(p)] \}_{t=0} = [ \alpha ( \frac{d x^\mu ( \lambda (t))}{dt})_{t=0} + \beta ( \frac{dx^\mu ( \kappa ( t))}{dt} )_{t=0}]
    I understand how these two lines are equal but how can we change the \phi's to x^\mu's in going from eqn 25 to the defn of Z_p(f)?

    b) where does eqn 27 come from? isn't ( \frac{\partial}{\partial x^\mu})_p (f) = \frac{\partial f}{\partial x^\mu})_p
    is it something like if we compose the numerator with \phi^{-1} then we have to cancel that out by composing the p with \phi to give the \phi(p)? I don't really get why this is allowed though?

    c)Where does eqn 29 come from?
    Attached Images
  1. File Type: pdfGR Course Notes.pdf (527.9 KB, 118 views)
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.