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題目如下, 請高手幫幫忙 ^^
1 G* w$ {% Y3 N) h8 Z1. 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. $ ~8 h; b0 a; @2 X9 X; @
' F4 V* T% n/ X0 e4 R/ r2.
' r; a! o" T) O" ya) 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.
. W3 [( t/ G' ^b) Write and test a program that computes f[n] using Module and a While loop.
1 H) T; d4 }( lc) 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.. q& O3 r: s7 ~: o
& E" `/ o( i' YConsider the iterative map Subscript[x, n] == 1/2 Subsuperscript[x, n-1, 2] -\[Mu]. " q4 s5 E" ?3 A( i& `
a) Compute its fixed points and 2-cycles as a function of \[Mu]." A2 f) m2 G8 x2 Z1 ^, ~; x% r
b) Using linear stability analysis, compute the range of stability of both the fixed points as well as the 2-cycles.
/ a: G# _" [0 Q, l+ K6 j2 g' hc) Show cobweb diagrams for representative parameters illustrating the (un)stable fixed point and 2-cycle.
2 j* j: V* n8 N3 [. |8 T# T0 gd) Graphically demonstrate the onset of a stable 3-cycle.
; P4 g, ]/ D2 i2 E C! p0 m: re) Produce the bifurcation diagram. |
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