lec07 notes

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+
+euler's method:
+
+dx/dt =~ ( x(t + Dt) - x(t) ) / Dt, for very small Dt
+
+so, x(t + Dt) = x(t) + f(x) * Dt, which is how to integrate the system
+
+"if Dt is too large, becomes highly unstable" (duh)
+
+scary MATLAB advice:
+- watch out of totally crazy values (very high)
+- non-negative values go negative
+
+MATLAB built-in ODE solvers: ode23, ode15s
+
+runge-kutta (use dxdt from between t_n and t_(n+1) )
+variable time-step methods
+
+summary: Euler's method sucks, news at 11.
+
+### misc julia notes
+
+the only place to find history (?!?!!) is in ~/.julia_history
+
+### codes
+
+using Winston
+
+a=20
+b=2
+c=5
+dt = 0.05
+tlast = 2
+
+iterations = int( round(tlast/dt) )
+xall = zeros(iterations, 1)
+x = c
+
+for i = 1:iterations
+    xall[i] = x
+    dxdt = a - b*x
+    x = x + dxdt*dt
+end
+
+time = dt * [0:iterations-1]'
+plot(time,xall)