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Type of Expansions and Differential Equations

  1. Feb 5, 2005 #1
    Hello all

    Could someone show me how we get: [tex] M(t+dt) - M(t) \doteq \frac{dM}{dt}dt + ... [/tex]. I know that you use a Taylor Series expansion, but I need to see how it is done as I am new in this subject. How would you derive the formula [tex] e^{-r(T-t)} [/tex]? Also could someone explain the concept of Seperation of Variables?

    Thanks :smile:
     
    Last edited: Feb 5, 2005
  2. jcsd
  3. Feb 5, 2005 #2
    I think I use a log expansion. Is that right?
     
  4. Feb 5, 2005 #3

    dextercioby

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    How about the definition of the derivative??

    [tex] \frac{dv}{dt}=:\lim_{\Delta t \rightarrow 0} \frac{v(t+\Delta t)-v(t)}{\Delta t} [/tex]

    For the second part,where does that exponential come from??

    Daniel.
     
  5. Feb 5, 2005 #4
    ok I get so we multiply by [tex] dt [/tex] to get the differential [tex] dM [/tex]
     
  6. Feb 5, 2005 #5

    dextercioby

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    Pretty much so.In this case "dt" is the one in the limit (Delta t,when it goes to zero).

    Daniel.
     
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