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[發問] 三個Mathematica的問題請求幫助

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fantuen

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电梯直达

1^#

发表于 2011-3-28 21:52 |只看该作者 |倒序浏览

|招呼Ta 关注Ta

請各位專家幫忙提示我該如何解題
感激不盡

Question.nb (5.6 KB, 下载次数: 2)

zan

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fantuen

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2^#

发表于 2011-3-28 22:37 |只看该作者 |招呼Ta 关注Ta

題目如下, 請高手幫幫忙 ^^
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.

2.
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.
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.

Consider the iterative map Subscript[x, n] == 1/2 Subsuperscript[x, n-1, 2] -\[Mu].
a) 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.
c) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle.
d) Graphically demonstrate the onset of a stable 3-cycle.
e) Produce the bifurcation diagram.