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題目如下, 請高手幫幫忙 ^^$ D, z1 J2 t S: g* C6 N
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. - ^5 H$ q4 I6 {9 l
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2. - F$ H8 A9 e9 L7 D+ B# i& W& v3 y
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.
2 F0 a+ G7 d9 D, j% ?. Vb) Write and test a program that computes f[n] using Module and a While loop.( S# S* q# N. }/ R0 n
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].
- v% m) S0 m+ n( A" va) Compute its fixed points and 2-cycles as a function of \[Mu].
7 [ }; V; r& d! @b) Using linear stability analysis, compute the range of stability of both the fixed points as well as the 2-cycles.
* `" a- a2 Q$ u# J0 I# Y, dc) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle.
2 K8 s7 L4 e: [# P' {3 Vd) Graphically demonstrate the onset of a stable 3-cycle.8 y6 Q/ z. E+ G0 ^- Z! I
e) Produce the bifurcation diagram. |
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