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題目如下, 請高手幫幫忙 ^^' W/ u3 t3 y. y9 K- w8 t' \/ G
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.
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2. * R6 ^0 l1 F) s: s4 o( W
a) 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.
- G9 m0 A: t; D' M8 Ib) Write and test a program that computes f[n] using Module and a While loop.$ u) g& m9 k, K3 F
c) 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.
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Consider the iterative map Subscript[x, n] == 1/2 Subsuperscript[x, n-1, 2] -\[Mu].
% O: c9 _& J6 q! Q5 la) Compute its fixed points and 2-cycles as a function of \[Mu]., z9 p9 _& C; d( Y9 I/ g
b) Using linear stability analysis, compute the range of stability of both the fixed points as well as the 2-cycles. ) @6 l2 W: }( P6 G+ h6 C6 D4 _
c) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle. * S$ ]& {1 n4 \: }& {
d) Graphically demonstrate the onset of a stable 3-cycle. X* C7 l4 W, N# J# v$ z$ E9 M4 B
e) Produce the bifurcation diagram. |
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