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Mathe III Lecture 5. Mathe III Lecture 5. Mathe III Lecture 5. Stability:. In the long run, the solution should be independent of the initial conditions. The general solution of. is:. if :. The system is stable. if. The root (s) are in (-1, 1) iff:. m. -1. 1. m. -1. 1.
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Mathe III Lecture 5 Mathe III Lecture 5 Mathe III Lecture 5
Stability: In the long run, the solution should be independent of the initial conditions. The general solution of is: if : The system is stable.
if The root (s) are in (-1, 1) iff: m -1 1
m -1 1 The system is stable iff:
Differential Equations Differential Equations First Order Differential Equations first order, ordinary equation (single variable)
x t
An approximation: For a given let: we obtain a difference equation , solve it and let or graphically:
For t = 0, assume x(0) = x0 x x2 x1 etc. x0 t
For t = 0, assume x(0) = x0 Now choose a smaller x x2 x1 As we approach a curve which solves x0 t
Separable Differential Equations A formal ‘trick’:
Separable Differential Equations (again)
Separable Differential Equations (again)
This enables us to study how the evolution of capital changes with the parameters