Mathematical Modeling

Homework Assignments

• Due Thursday, January 24
  # 2.3 p. 6; 5.2 p. 15; 5.5 & 5.6 p. 16; 6.2 p. 18;
  # 10.1 & 10.5 p. 32; 11.2 p. 34; 13.1 p. 41; 13.6 p. 42

• Due Tuesday, January 29
  A description of your project, indicating what you want to model, how you will obtain the data, and how you plan to get started. The report should be typed.

• Due Thursday, February 7
  # 18.3 p. 59; 18.10 p. 61; 19.4 p. 66; 21.1 p. 75; 21.7 & 21.8 p. 76; 24.1 & 24.3 p. 86; 26.8, 26.10 & 26.13 p. 99; 27.3 p. 103

• Due Thursday, February 21
  
  • # 15.2 p. 52; 22.2 p. 81; 23.4 p. 84; 28.7 p. 113
  • An introduction to your project, including background information, what you are going to model, and how you plan to proceed. The report should be typed and should contain figures and all of the relevant information.
  • Find the value of a at which the period-2 cycle of the logistic map becomes unstable.

• Due Thursday, March 7
  # 32.15 p. 129; 33.1 p. 130; 34.1, 34.3 & 34.4 p. 135; 34.7 p. 136; 34.16 p. 137; 37.4 p. 155; 38.2 & 38.3 p. 158; 39.4 p. 161

• Due Thursday, March 28
  # 36.4, 36.5 & 36.6 p. 151; 40.2 p. 170; 40.6 p. 171; 41.1 p. 177; 42.13 & 42.16 p. 184

• Due Thursday, April 11th
  # 44.3(i) p.190; 45.2 p. 199; 46.4 p. 203; 49.2 p. 227; 50.12 & 50.13 p. 241; 51.2 p. 243; 54.3 & 54.5 p. 254

• Due Thursday, April 18th
  A progress report on your project. This should contain an updated introduction section with relevant background information as well as a description of the modeling work you have done so far. Include all relevant information (things which you tried and did not work, if any, should be discussed). Also, if you want me to comment on various ideas/points which you may want to pursue in your final report or presentation, make sure you discuss them (at least briefly) in this progress report.

• Due Thursday, April 25th
  A one- to two-page report on one of the following papers:
  • A.U. Neumann et al., Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy, Science 282, 103-107 (1998).
  • P.J. Hudson, A.P. Dobson & D. Newborn, Prevention of population cycles by parasite removal, Science 282, 2256-2258 (1998).
  • G.F. Fussmann, S.P. Ellner, K.W. Shertzer & N.G. Hairston Jr., Crossing the Hopf bifurcation in a live predator-prey system, Science 290, 1358-1360 (2000).
  • C. Sachs et al., Spatiotemporal self-organization in a surface reaction: from the atomic to the mesoscopic scale, Science 293, 1635-1638 (2001).
  The report should describe the mathematical model used in the paper, give enough background information to understand its derivation, and summarize the results. Your presentation should explain how ideas discussed in class (such as scalings, fixed points, and linear stability analysis) are used in analyzing the model.
  Members of a same team MUST work on different papers.

• Due Thursday, May 9th
  Your written final report.