Science One: Mathematics site
Suggested problems
Note 1: The following list of problems is intended to serve as a guide to the types of problems that will be useful in learning the material. YOU SHOULD KEEP DOING PROBLEMS UNTIL YOU ARE CONVINCED YOU UNDERSTAND THE MATERIAL, EVEN IF YOU DO ALL THE PROBLEMS LISTED HERE!!
Note 2: Problems not from the textbook will occasionally be posted on the "handouts" page.
Note 3: some of the listed problems require a graphing calculator. Such questions will not appear on midterm and exams but may be useful nonetheless in learning concepts.
- Chapter 2
Problems from 2.1: #1-8.
Problems from 2.2: some of #1-12, 13, 16, 17, 19, 23, 26, 32, 37, 40.
Problems from 2.3: #1, 2, 3, 7, 9, 10, some of 11-30, 36, 37, 40, 43, 46, 49, 56, 58, 62.
Problems from 2.5: #3, 5, 6, 9, 13, 16, 20, 22, 27, 36-41, 46, 49, 51, 56 (I'm not sure what "(6)" refers to but you should be able to do this anyway), 64, 65.
Problems from 2.6: #3, 5, 8, 14, any of 15-36, invent a problem like 47 but with different values (chosen randomly) and answer it, 54b, 55, 58, 59.
Problems from 2.7: All look good. I really like #12, 17, 20, 31-36. And 21-24 are pretty standard ones that you should be able to do in your sleep. Also try a few of 39-47.
Problems from 2.8: #3, 14, 16, 19-29, 33 (part b should say "approximate" somewhere), 34, 35-38, 41-44, 48.
Certainly do a bunch of problems from the review list. - Chapter 3
Problems from 3.1: DO PROBLEMS.
Problems from 3.2: DO PROBLEMS.
Problems from 3.3: DO PROBLEMS.
Problems from 3.4: DO PROBLEMS.
Problems from 3.5: DO PROBLEMS.
Problems from 3.6: DO PROBLEMS.
Problems from 3.7: Do many; be sure to try #13, 14, 17, 27, 31.
Problems from 3.8: Do many; be sure to try #2, 3, 5, 11, 16, 18.
Problems from 3.9: If you can't do the harder ones, try the easier ones first, then try the hard ones again. The problems (allegedly) get harder toward the end of the exercise section.
Problems from 3.10: #17, 20, 23-28, 37, 40. - Chapter 4
Problems from 4.1: #1, 3, 5, 8, 11, 22, 28, 34, 35, 40, 45, 56, 62, 63, 70 (design an experiment to test this), 73, 75.
Problems from 4.2: DO PROBLEMS.
Problems from 4.3: #3, 6, 7, 12, 14, 20, 28, 35, 54, 62, 63, 64, 66, 73, 74 (give an example where it works, where it doesn't), 77.
Problems from 4.4: #1-4, some of each type from 5-64, 69, 70, 71 (annoying, isn't it), 73, pick a favourite from 74-84.
Problems from 4.5: try some of each type from 1-52 (polynomials, rational functions, trig, exp and log), 55, 56, 58, 65, 70, 72. Problems from 4.7: # 5 + n*7 for n=0,1,...,7.
Problems from 4.8: 1, 2, 15, 29, 39. - Chapter 9
Problems from 9.1: #1, 3, 6, 7 (you'll have to figure out the derivative of ln(x)), 9, 10 (constant solutions are precisely steady states), 11.
Problems from 9.2: #1-14, 18-24.
Problems from 9.3: 1, 2, 3, 4, 5, 10, 11, 12, 14, 19, 21, 38, 39, 40-44, 46. Note: none of these require anything more than doing a "backward chain rule". Some might have to be left in implicit form.
Problems from 9.4: More good modeling problems - try a bunch of these. - Chemistry text - chapter 14
1 [write down a DE for A(t), B(t), C(t), and D(t)], 2, 3, 4, 7 [for (b), explain why it is ok to assume the rate is unchanged throughout 1 minute], 15, 16, 17-26 [for each of these, write down an IVP for A(t)], 27-29, 33 [write down an equation for A, B, C, and D], 34.