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Solve this problem by a method like the one used above and find the corresponding formula for x(t,0). ) 42 5. Unsymmetrical component of the response We have found the symmetrical component V of the response to a single injection of current at a synapse. This depends only on the non-dimensional distance of the synapse from the cell body. At the cell body itself V = V, so we have found the response. In the rest of the dendritic tree no such formula holds (except for a symmetrical distribution of inputs).
63) in the limit s - 0. This will be done by finding a formula for the propagation speed of the fronts. By "front" we. mean the place where a tran:,itior, in m from 0 -> 1 or 1 - 0 occurs. :urge in the x,t plane along which a jump in m occurs.
The Heat Equation. Let v(t,xl ... xn) = v(t,X) be the soultion of (at - A)v(t,X) = f (t) S (x1) ... 52) ( at + at - A)vc(t,X) = f(t)S(xl) ... 55) atvc = (at - Choose a = a2/2. 56) And )uce-at at2 -a- 4a) uc (t,X) = f (t) eXtd (xl) = f (t) 27 e(c. (xl) ... 60) ... 36) with k = is/2 and with f (1) eCT/7 instead of f (t) . 63) C2 R yff1 f(t - R)e C R2-r2 Let R = ct'. t_ Equation in two dimensions. ing solution in n dimensions. 29 Exercises Consider the system of equations! au + C ax = 7 v(v-u) 9v -c 8t = u+v.