IMPORTANT: See the syllabus regarding the final and the projects. In particular, read that before looking at the solutions for homework you haven't turned in yet!

RECENT: Arnold's cat Mathematica notebook (or html `hardcopy') from class and cat sketching hints (notebook or html `hardcopy') for homework.

Homework 1 (due 10/7):
1.1) 1, 2, 5, 6, 19, 21
1.2) 1, 3, 41
1.3) 7, 8, 9, 12, 13, 15
1.6) 1, 4, 7, 13, 16, 19, 30, 31, 33, 35, 44

Note: I think the problems from 1.6 should be mostly visual work, not pencil and paper work (except for 44), but if I'm wrong about that, or if they're taking too much time for any reason, let me know. I'll always give you at least a week to do any assigned problems. Until I have some feel for everyone's backgrounds, and hopefully some idea of a reasonable pace for the lectures, I prefer to assign little by little, trying to avoid having the homework lag too far behind or, worse, get ahead of the lectures.

Below are links to the first homework problems, scanned in from the text, in case you haven't gotten the book yet. (I won't do this every week!)
Note that there are parts of pages that you won't need; only do the problems assigned above.
Section 1.1 (1.1a, 1.1b, 1.1c, 1.1d, 1.1e), Section 1.2 (1.2a, 1.2b), Section 1.3 (1.3a, 1.3b, 1.3c), Section 1.6 (1.6a, 1.6b, 1.6c, 1.6d).

Hint for problem 41:
In case #41 is causing a little trouble, try the following: Use the solution of the Initial Value Problem (IVP) from the first lecture, or verify that the general solution is M(t) = c e^(i t) + p/i for some constant c and find c from the initial data M(0) = M_0, where M_0 will be the initial amount owed. Now use the fact that a thirty-year mortgage is will be paid off in thirty years, i.e. M(30) = 0, to find the annual payment p. (This aspect of the problem is like a Boundary Value Problem (BVP).) Now, if you're paying p per year, figure out how much you'll have paid after thirty years. For part c), do a standard introduction to the exponential calculation to figure out how much Ms. Lee's $4500 investment would be worth after thirty years.

Remark about real-life mortgage choices: These days it's quite rare for someone to keep their mortgage for the full term of the loan. More often, they either refinance or sell the property before the 15/20/30 years have elapsed. Also, the Federal tax deduction of the interest paid on home mortgages further clutters the situation. Rates of return on investments typically vary with time, while inflation and changing earning power alter the effective value of money over extended periods of time. ($20 probably seems like a lot less money to you now than it did ten-fifteen years ago, and will probably seem like even less in another few years.) If you have a few spare minutes, mull over the possible parameters that might go into a more detailed model of mortgage costs. A relatively simple calculation might be to determine which loan option is a better deal for Ms. Lee, using the model given in #41, but assuming that she sells the property after ten years. (You'd need to figure out both how much she'd paid and how much of that money actually went towards the principal (i.e. the money actually borrowed), not just to paying interest. On a thirty year loan the size of Ms. Lee's, you could just about buy a pizza with the amount you'd paid on the principal in the first year, if I'm remembering my old mortgage statements correctly.)

Solutions for the first assignment
Section 1.1 (page 1, 2, 3), Section 1.2 (page 1, 2, 3), Section 1.3 ( page 1, 2), Section 1.6 ( page 1, 2, 3).

Homework 2 (due 10/14):
1.7) 1, 5, 7, 9, 12, 13, 20, 21
2.1) 1, 2, 8-11, 17
2.2) 1, 5, 7, 9, 11, 13-16
Note: Many of the problems in this homework set are primarily visual, e.g. "match this kind of plot to that kind of plot, or match the plot to the equation". If they're taking a huge amount of time, let me know.

Solutions for the second assignment
Section 1.7 (page 1, 2, 3), Section 2.1 (page 1), Section 2.2 (page 1, 2).

Homework 3 (due 10/21):
2.3) 5, 6, 13, 14, 19
2.4) 1-6
3.1) 10, 13-16, 24, 27, 34

Solutions for the third assignment
Section 2.3 (page 1, 2), Section 2.4 (page 1, 2), Section 3.1 (page 1, 2, 3, 4).

Homework 4, part I (due 10/28):

Read the hand-out from Arnold's Ordinary Differential Equations. Skim over parts involving advanced analysis, e.g. convergence of the infinite sum, if you're not familiar with that sort of argument. Read "matrix" for "linear operator" if you prefer.
Choose two 2x2 and two 3x3 matrices (not diagonal!). Compute their eigenvalues, find eigenvectors for those eigenvalues, and compute the matrix exponentials of the matrices.

Homework 4, part II (due 10/28):
3.2) 4, 12, 16, 17, 19
3.4) 2, 10, 12, 13, 19

Solutions for the fourth assignment
Section 3.2 (page 1, 2, 3), Section 3.4 (page 1, 2).

Homework 5, part I (due 11/4):

3.3) 20-27
3.4) 1, 4, 11, 14

Solutions for the fifth assignment
Section 3.3 (page 1, 2, 3, 4, 5, 6, 7, 8), Section 3.4 (page 1, 2, 3).

Homework 6 (due 11/18):

Sketch the image of Arnold's cat under the linear transformations appearing in the following exercises from the text: 3.2) 1, 3, 7 and 3.4) 3, 5, 9. Determine whether the area of the cat increases or decreases under the transformation.

3.5) 1, 4, 5, 8, 9, 12, 14

Solutions for the sixth assignment
Arnold's cat: Mathematica notebook or HTML file.
Section 3.5 (page 1, 2, 3, 4).

Homework 7, part I (due 11/25):

3.7) 1, 2, 4, 7, 8, 10, 11

Solutions for the seventh assignment
Section 3.7 (page 1, 2, 3).

Homework 8 (due 12/2):

5.1) 1-4, 6, 10, 18, 28-30
5.2) 1, 2, 4, 7, 8, 15, 16, 18

Solutions for the eigth assignment
Section 5.1 (page 1, 2, 3, 4, 5), Section 5.2 (page 1, 2, 3).

Project Proposal (due 11/18):

The proposal for your (optional but strongly recommended) final project should be approximately one page in length. (Longer is OK.) You should describe the subject you intend to study; why the subject is interesting, important, and relevant to the course; what you intend to do; possible resources (text, outside texts, research papers, software); likely challenges. Be as precise as possible in describing your goals. It's OK to do more than you anticipated, but a grandiose proposal without good follow-through is not desirable.

Possible sources of topics:

Sections of the text that we haven't covered (check with me to see if we will definitely be covering them in the future). We'll do section 5.1-4 in class; also 6.1 and, if there's time some material from the start of Chapter 4. However, Chapters 4 and 6, as well as 7 and 8, are fair game for a project, as long as you go beyond the first section of the chapter.
Material from other courses you're taking, as long as you relate it to dynamical systems.
Material from other ODE/dynamical systems texts.