29::196 Computational Physics: Assignments  for week 2

Tasks: draw cobwebs, histograms, calculate Lyapunov exponents and entropy for various discrete dynamical systems.
Click here for homemade histogram


Suggested Readings: ZO:  Chapter 5 (the source file is available in version 5 ); GN:  section 3.7

Problem set: ZO Chapter 1,  Problems  19, 21, 22 (assume an infinite sheet or pick boundaries) and 24 (solve it by brute force, averaging over random samples, and compare with a logical answer); Chapter 5: Problems 2 and 5 (page 297). 
Additional problems:
A) in problem 1.1.b in ZO (last week's first problem), show algebraically that the roots are real.
B) Draw the level curves of the real and imaginary parts of f[x_] := beta*x + (1/2)*(Log[x] + Log[2 - x]) for 2 complex values of beta =0.1+0.4*I;
find the singular points where the complex derivative vanishes. Discuss the behavior near these points, 0 and 2. Draw a nice picture.

email the notebook to ymhw09@gmail.com  no later than Tuesday 2/10/09 (two weeks from now). No late work.