suplecture3 - Supplemental Lecture 3 Differential Equations...

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Supplemental Lecture 3 Differential Equations
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III - 2 Differential Equations Let f : R n R . The equation is an n th-order differential equation . = - - 1 1 ) ( , , ) ( ), ( ) ( n n n n dt t x d dt t dx t x f dt t x d
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III - 3 Complete Specification To complete the problem, we need to specify initial conditions x (0), dx (0)/ dt , . . . , d n - 1 x (0)/ dt . A solution to the differential equation is a C n function x : R R that satisfies the initial conditions and such that the derivatives satisfy the differential equation for all t . There will be a unique solution to this problem.
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III - 4 Numerical Approximation We can obtain a numerical approximation to the solution as follows. Choose a step size t > 0. x ( i ) ( t ) will be an approximation to d i x ( t )/ dt for i = 0, . . . , n . x (0) ( t ) approximates the solution x ( t ).
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III - 5 Computing the Approximation For i = 0, . . . , n , let For j 0, assume we have defined x ( i ) ( j
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.

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suplecture3 - Supplemental Lecture 3 Differential Equations...

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