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.