Section 2.1: #1-6 (these go together), 7 (also sketch the R(t) and F(t) graphs), 9-14 (these go together), 15, 16, 17, 19, 20. Be sure to read all of these problems and attempt most of them. Be sure to do 19 and 20 (they are second-order equations). On some problems, guess with a reason, check the answer in the back of the book, then explain the answer in the book if it's different from yours. Use ODEs.nb to "solve" some of the systems and draw their solution curves. Add equilibrium points and flow curves approaching and leaving them to get a reasonably complete view of the phase planes.Section 2.2: #3, 4, 5, 7 (second-order), 9, 10, 11, 13, 15, 18, 21 Use ODEs.nb to draw some of the vector fields solution curves. Add equilibrium points and flow curves approaching and leaving them to get a reasonably complete view of the phase planes.Section 2.3: #1, 2, 5, 6, plus the following three using the same instructions. The same process doesnt quite work in two of them, but carry through as far as you can. We will see how to complete them in Chapter 3.Section 2.4: #1-4, 5, 6, 7, 10, 13Section 2.6: #1, 2, 6, 7, 11Section 2.7: #2, 7 Use 2.7.SIRmodel.nb to answer these.--------------------------------------------------Section 3.1. Reading: There is a lot in this section, however, a good bit of it is linear algebra review. If you remember how to multiply matrices and compute the determinant of a 2x2 matrix, it will go quickly. You might even see a null space pop up (although the authors don't use this term)! Problems: #5, 7, 9, 11 & 13 (use Mathematica), 16 & 17 (do together), 24 - 29 (do at least three)

Section 3.2: 1-14 (Do at least five, at least two from 11-14), 20 (read 19), 21 - 24 (do two) You may use Mathematica to compute eigenvalues and eigenvectors (the command is Eigensystem), but you should also know how to do this by hand. Read 15-18. These are some linear algebra facts, at least some of which should be familiar.Section 3.3: Reading: Note the fully decoupled systems used as simple examples on pages 281 and 285. You can skim the coffee-tea example at the end. Problems: 1-16 (Do at least five. These continue 1-14 from 3.2.), 19, 20, 21Section 3.4: #1, 2, 3-8 (do at least three), 9-14 (do at least three), 15, 23, 26 Problems 3-8 illustrate how much information you can get just from the eigenvalues. You may use Mathematica to compute the eigenvalues, but you should be able to compute them by hand also. For part e), use VectorPlot in Mathematica with the StreamLines option. Skip drawing the x(t) and y(t) graphs. In problems 9-14, use Mathematica to find the eigenvectors and to draw the x(t) and y(t) graphs.Section 3.5: #1-4 (do at least 2), 5-8 (do at least two), 10, 11, 17-19 (do at least two), 21, 22, 24 In 1-4, use Mathematica for part (c) to draw the vector fields.Section 3.6: #1-12 (at least four), 13-20 & 21-28 (at least four from each group) The "Free Gift" is that you can write down the general solution of y" + py' + qy = 0 without having to find the eigenvectors or even converting it to a system. In 1-12, be sure to get a variety of real, complex, and duplicate eigenvalues. Note that the problems in 13-20 repeat in 21-28, but with different questions. Be sure you can do the computations by hand. You may use Mathematica to draw the graphs. Read 30, 31, 32. The last one is worth noting because it tells you what a corresponding eigenvector is. Warning: This is valid only for the systems that come from a second-order linear equation. Physics majors and engineering students should read 36, 38, 39, 40!Section 3.7: #2-7 (at least three), 8-10 (do at least one), 11-13 (read all, do at least one) #2-7 are similar to what I was doingat the end of class. The discussion and pictures in the book indicate why the saddle is a bit hard to see: the eigenvectors (which give the straight-line solutions) are close together. In 8-10, if you see how the parameters a and b are related to T and D, you won't have to analyze the ab-parameter plane from scratch. Engineering students should consider the significance of 11-13. The behavior of the suspension system in a car can change qualitatively (go through a bifurcation) if the mass changes (think about overloading a pick-up truck), or the car ages (the springiness of the struts and the viscosity of the damping fluid in a shock absorber can change).