A general second-order difference equation takes the form xt+2 = f (t, xt, xt+1). As for a first-order equation, a second-order equation has a unique solution: by successive calculation we can see that given x0 and x1 there exists a uniquely determined value of xt for all t ≥ 2. (Note that for a second-order equation we need two starting values, x0 and x1, rather than one.) Second order linear equations Consider [...]
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Second-order difference equations
Posted in Math on 十一月 18, 2008 | Leave a Comment »
Integration by part
Posted in Math on 十一月 13, 2008 | Leave a Comment »
A very useful technique for evaluating integrals is Integration by Parts: It is derived from the product formula for derivatives. Sometimes it is more convenient to express this formula using differentials:
