LIFESCI 30A Lecture Notes - Lecture 10: Differential Equation
28 Oct 2016
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A restriction mostly seen in 2 dimensional state space. A lot easier to deal with in a 3 dimensional state space because it can loop in and around. If it ever intersects itself, it must be periodic. (one curve is approaching another curve asymptotically) Next state = current state + dt[change vector] For a 1-variable differential equation x" = f(x) state is just x. Later x=current x at x" (and the smaller dt is, the better this approximation is. ) Later x current x = dt * x". Now x" = (later x current x) / dt and again the smaller dt is, the better the approximation. The expression above is actually called the average rate of change over the time interval described by t (take the limit) X^3 curve where origin is about 5,5 and 2 points meet with (t1, x(t1)) to (t2, x(t2)). Average rate of change over the time interval from t1 to t2 is .
