3 y- q: w; f1 \9 K作者: fantuen 时间: 2011-3-28 22:37
題目如下, 請高手幫幫忙 ^^: U5 ~2 d3 i8 o, H" D5 H
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. ( p! K* ^4 f' y, q. [" l1 j2 G: F+ ^: B% r p
2. 3 P( \- K! l* ~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.4 ~' w6 {- b* c* P; n/ V
b) Write and test a program that computes f[n] using Module and a While loop. + j9 G' \+ ~5 E# \$ w9 n* B( Jc) 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. 2 U, }/ b7 |: b* y6 N" R8 S+ @( Y, m6 c1 d% z9 o) V
Consider the iterative map Subscript[x, n] == 1/2 Subsuperscript[x, n-1, 2] -\[Mu]. 4 M8 t( W6 Q* F. K
a) Compute its fixed points and 2-cycles as a function of \[Mu]. + ]1 i9 V5 N3 g7 w9 z+ @b) Using linear stability analysis, compute the range of stability of both the fixed points as well as the 2-cycles. " ]0 |2 j2 E& Q0 l7 kc) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle. 6 s: }/ k0 t! N) `5 }: y- Ed) Graphically demonstrate the onset of a stable 3-cycle. # b% Q/ i P3 s7 A5 }e) Produce the bifurcation diagram.作者: fantuen 时间: 2011-3-28 22:40
似乎貼的不是很好...% W' n. Q: K7 `# O, h
如果有達人願意幫忙, 麻煩+我QQ 860288311 6 G& c( |" u2 U4 _& y# A我可以把notebook檔案發給你作者: gaoshanliu水 时间: 2011-3-29 13:35
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