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題目如下, 請高手幫幫忙 ^^2 N5 D0 g0 M& {; U9 z
1. Write a function that as input has an expression f, and returns the logarithmic derivate 1/f (d f)/(d x) . Use a conditional or pattern test to make your function accept any symbols as input except for lists.
( o F d' M3 J- ]7 |9 [4 C6 k; w, K
2.
( Z9 F, S, H( G; v& x0 x8 Y/ K% Fa) Write a recursive function that computes the function f[n] defined by 6 n f[n]=f[n-1]+n! for n>0, and f[0]=7. Restrict the argument to positive integers.
+ M/ A; v* M n' Y2 _8 U5 kb) Write and test a program that computes f[n] using Module and a While loop.
( G; G3 Y- Y5 c- Qc) Compare the timings of the two methods by computing f[n] in both cases for very large values of n and/or doing the computation many times. You may have to use Clear or restart to clear Mathematica's memory of previous calculations. Explain your results.
* \& W' D2 n0 e2 `& \( Q7 _9 Z! h/ ]
Consider the iterative map Subscript[x, n] == 1/2 Subsuperscript[x, n-1, 2] -\[Mu].
* [0 W) |- g, X, F; n% ba) Compute its fixed points and 2-cycles as a function of \[Mu].* ]& |$ J5 B# n( o8 q
b) Using linear stability analysis, compute the range of stability of both the fixed points as well as the 2-cycles.
! k0 i/ S/ Q+ g; C, ~c) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle.
! [8 G5 I, p' j- P, t, ud) Graphically demonstrate the onset of a stable 3-cycle.7 G# _5 Q1 ^1 n/ M$ _& q
e) Produce the bifurcation diagram. |
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