[發問] 三個Mathematica的問題請求幫助

fantuen

請各位專家幫忙提示我該如何解題
' D' r% Z, O& X! N, O感激不盡
; e) L/ B; m4 t
6 b& i! g; X: s4 |2 U Question.nb (5.6 KB, 下载次数: 2)

2011-3-28 21:51 上传

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gaoshanliu水

fantuen

似乎貼的不是很好...
1 _/ x2 y8 [( u9 E$ ~& }% O如果有達人願意幫忙, 麻煩+我QQ 860288311
我可以把notebook檔案發給你

fantuen

題目如下, 請高手幫幫忙 ^^
9 q: y: {. u# |( x! `! e/ r1. 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.
, u# j/ K! f, T! Q' `. ]6 f: M
8 v* W0 x  z3 r" h* ^2.  
4 S+ q; ~2 Z9 Q. Da) 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.
b) Write and test a program that computes f[n] using Module and a While loop.
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.
5 M9 A$ ~" L. x1 x6 \
2 O8 u( R+ `4 zConsider the iterative map Subscript[x, n] == 1/2 Subsuperscript[x, n-1, 2] -\[Mu].
9 K+ Q9 e- e* `4 O# \. N4 c5 Xa) Compute its fixed points and 2-cycles as a function of \[Mu].
b) Using linear stability analysis, compute the range of stability of both the fixed points as well as the 2-cycles.
% S+ Q  P: w- J4 Vc) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle.
2 g9 E+ I) s& g/ i1 Hd) Graphically demonstrate the onset of a stable 3-cycle.
e) Produce the bifurcation diagram.