ku Posted February 19, 2006 Share Posted February 19, 2006 [math]m_{t+h}-m_{t}=hm_t[/math], so [math]\frac{dm_t}{dt}=m_t[/math] I am told that you use differential equations to the get the differentiation above, but I don't see how. Can anybody see? Link to comment Share on other sites More sharing options...
the tree Posted February 19, 2006 Share Posted February 19, 2006 Does any of it mean anything? What type of set is m? Link to comment Share on other sites More sharing options...
SilentQ Posted February 19, 2006 Share Posted February 19, 2006 Y'what? The first equation is not internally consistant. [math]m_1=2m_0[/math] So far so good. Now derive [math]m_2[/math] directly from [math]m_0[/math], whatever it may be. [math]m_2=3m_0[/math] But deriving it from [math]m_1[/math] above, we run into a contradiction. [math]m_2=2m_1=4m_0[/math] The second equation implies that [math]m_t=e^t+a[/math]. Link to comment Share on other sites More sharing options...
Tartaglia Posted February 24, 2006 Share Posted February 24, 2006 It really should go something like this Let m(t) be a function of time and let h be a small increment of time m(t+h) - m(t) = hm(t) divide through by h (m(t+h)-m(t))/h = m(t) Take limit of LHS as h tends to zero ie h becomes a infinitesimal change in time dt and m(t+dt) - m(t) = dm(t) ie dm(t)/dt = m(t) I suspect this is some sort of Markov process Link to comment Share on other sites More sharing options...
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