18.385J | Fall 2014 | Graduate

Nonlinear Dynamics and Chaos


This course makes use of Athena, MIT’s UNIX-based computing environment. OCW does not provide access to this environment.

Assignment Policies

There are 10 problem sets during the semester (one every 1–2 week, more or less).

  • Collaboration: It is Ok to exchange information with other students, in the sense of hints, general ideas, pitfalls to avoid and so on; i.e.: “within reason”—“let me see / copy” your answer is not within reason. But, the final answer must be written 100% alone, with understanding of every dot that goes in there.

Warning: You are 100% responsible for any answer you supply in a problem set, or (for that matter) in the term paper. I can call you any time to explain your answer. If I am not convinced that you understand what you wrote, you will lose credit, up to and including losing credit for the whole problem set, depending on degree of lack of understanding. In the case of the term paper, this could make it “not-acceptable.”

  • Warning-Warning-Warning-Warning-Warning — Clarity: Your answers must be presented in a way that is easy to read. Type them (12 point) or, if by hand, write clearly, use a large enough font, and high contrast ink or pencil. The lecturer has serious trouble reading stuff not following these simple guidelines. Material that fails these readability requirements may end up with no credit given.

For that matter, this being a graduate student level course: Graduate student level of explanations will be expected. To get full credit, the arguments have to be clear, complete, and in reasonably good English.

As for the level of rigor: “math proof level” is not expected. The same level as in the lectures, book, or notes (“reasonable scientist”) is the expectation.

  • Note that only the “quiz-problems” will be graded in each problem set. Since these will not be announced, you should do all the problems—if you happen to miss them in your answer, you will get zero credit, even if you did the others. Answers will be provided for all the problems.
  • Any “suggested reading”, “suggested problems” and any other “suggested” are for you alone to do or not do. Thus: Do not hand in these problems!
  • About Computer Assignments (if any):
    • Use any language or computer you like. Athena accounts are available to all students. I recommend MATLAB®, which is available in Athena. Better yet: Get the Student Edition of MATLAB®, and port the Course Software there. In Athena you can find “dstool”, but it’s harder to use. MATLAB® or Mathematika are easier to use and more flexible. You can also use C, Fortran or whatever works for you.
    • Include brief explanations of how the problem was solved (a printout of a program is not enough!). I want to know what is the idea!
    • Results must be condensed to some comprehensible and concise form:
      • Use plots, tables or graphs. Do not show “raw” numerical output.
      • Make sure one does not have to hunt for the answers all over the place. They must be easy to find and identify. Put them at the beginning, for example, and then justify them.
    • Include a printout of your program appended (at the end)—if there is one. If you used “canned” software, state which one, and spell the numerical parameters and other such data used—these things usually give you a choice of time step, numerical method, etc. I do not want to see such things used as “black boxes” with default parameters. I want you to think, and know, what you are doing.
    • Look at your output and make very sure it makes sense! That a program “runs” does not mean it does so as intended. For example, if you are using too large a time step, you will still get some output… which can easily be nonsense!

Problem Sets

Problem Set 1 (PDF)

Problem Set 2 (PDF)

Problem Set 3 (PDF)

Problem Set 4 (PDF)

Problem Set 5 (PDF)

Problem Set 6 (PDF)

Problem Set 7 (PDF)

Problem Set 8 (PDF)

Problem Set 9 (PDF)

Problem Set 10 (PDF)

Course Info

As Taught In
Fall 2014
Learning Resource Types
Problem Sets
Lecture Notes