Homework |
Only the boldface problems will get graded, but you should turn in all problems. The non-boldface problems are as important as the boldface ones. The only reason some are bold and some aren't is that the grader doesn't have time to grade all of them. But you should know how to do all of them.
HW # | Due Date | Read | Do |
---|---|---|---|
Final Exam | F 5/9 6:30-9:30 pm, Fowler 302 |
Start reviewing for the final two weeks in advance. Here are some review problems. | Do not turn in: Ch 6 review exercises: 13, 15 (hint: look up derivative of arcsec), 22, 33, 36, 40-42, 54, 58, 62-64, 66, 68, 79, 84, 89, 90, 102b. Solutions Ch 7 review exercises: 6abcfg, 7, 8, 11, 12a, 14a, 18-20. Solutions Ch 8 review exercises: 1-11, 14, 41, 42, 47-53. Solutions Ch 10 review exercises: 1-5, 7-11, 15-29, 31, 34-37. Solutions |
29 | W 4/23 | Sec 10.10 (may skip Example 5 and "Modeling Physical Laws with Taylor Series"). We rushed through the book's Example 4, so read it carefully. | Sec 10.10: 1, 2, 5, 11, 13,
21a, 25, 26, 33, 34a, 35a. Use table on page 701. Solutions |
lab test Solutions |
4/22 |
Here's a sample test. The test will include questions on Mathematica as well. See HWs 18 and 19, and labs 2/26/08 and 3/18/08. | |
28 | M 4/21 | Sec 10.8 (all). | Sec 10.8: 19-26, 30, 47, 49,
50. Solutions |
27 | F 4/18 | Sec 10.8 up to "Finding the Interval of Convergence." | Sec 10.8: 1, 3, 5, 6, 11,
15, 17. Solutions |
26 | W 4/16 | Sec 10.7 up to "The nth Remainder" | Sec 10.7: 3, 5, 6, 11,
21, 25, 26, 34, 35. Solutions |
25 | M 4/14 | Sec 10.6 (all). Also read this. | Sec 10.6: 11, 12, 17-19, 22,
23, 25, 26, 47, 48, 53, 55a. Bold: all evens. Solutions |
24 | F 4/11 | Sec 10.6 up to Absolute Convergence | Sec 10.6: 1, 2, 3, 6,
31, 33, 35, 39. Sec 10.5: 52. Solutions |
Mid 3 with solutions | W 4/9 | Covers HWs 14-23. Start reviewing and redoing homework problems (without looking at solutions) a week in advance. | Optional: Do these only if you want more practice with
Chapter 10; do not turn them in. Chapter 10 review problems (page714): 1-3, 9abe-j, 11, 15-19, 20a. Solutions |
23 | F 4/4 | Sec 10.5: Ratio Test and Root Test | Sec 10.5: 11-13, 19-20, 30,
38-41. Bold: 12, 30, 40, 41. Hint for 40: ln k < sqrt(k) for every k > 0. Solutions |
22 | W 4/2 | Sec 10.5 up to The Ratio Test. Also review problems 15-20 of Arithmetic with large and small numbers of HW #13 (do you remember how to do them without looking at the solutions?); they are very helpful when using the limit comparison test. |
Sec 10.5: 1-10. Bold: 2a,
3b, 4b, 7, 9. Solutions |
21 | M 3/31 | Sec 10.4 pages 654-656. The proof presented in class for the Integral Test may apprear on exams. (The proof given in the book is similar, but more rigorous, and hence harder to read. If you understand the "class proof", that's good enough.) |
Sec 10.4: 3, 7ab, 11,
13, 14, 22, 23, 25, 26, 28, 30, 31abc. Solutions |
20 | F 3/28 | Sec 10.4 pages 652-654. | Sec 10.4: 1, 2, 5, 6, 9,
10, 15, 17, 18, 21, 27, 29a. Hint for 2: k^2 -1 = (k-1)(k+1) Hint for 21: Use divergence test; do L'Hopital twice. 27: the proof won't be on exams, but you should understand what the problem is saying, so that you can use it for 29a. (And if you can do the proof, good for you! You have a good intuition for logic.) Solutions |
19 | W 3/26 | Sec 10.3 page 648. | Sec 10.3: 6, 7, 8,
11, 12, 13, 17, 19, 21, 25a, 28, 34a. Also turn in all of these extra problems, on Excel/Mathematica Syntax Solutions |
18 | M 3/24 | Sec 10.3 pages 643-647. | Sec 10.3: 1, 3, 5, 22,
23, 24, 26, 27, 38. Use Mathematica for #38. Go to any computer lab in Fowler before 5pm. Library computers too may have Mathematica on them; you can call ITS at x2880 to help you install Mathematica on any campus computer -- takes only a couple of minutes). Solutions |
17 | F 3/21 | Sec 10.1 pages 624-630. | Sec 10.1: 1, 4, 5, 7, 8,
11, 13, 16, 18, 19, 21, 29, 33, 34. Solutions |
16 | W 3/19 | Sec 9.1: pages 582-583, 586 (bottom), 587-588. | Practice problems for
indeterminate forms: turn in all of them; short answers OK. Also do: Sec 9.1: 1, 3, 5, 17, 19, 23, 26, 27, 29, 39. Hints for #23: for integral of 1/sin(x), look up table of integrals inside the book's front cover (look for csc(x)). Also, 1 / (y^2 - y) = 1/(y-1) - 1/y. For #5, review implicit differentiation from last semester (page 237), if you feel rusty. Solutions Solutions to Practice problems for indeterminate forms |
Lab | T 3/18 | Read pages 545-546. | Do not turn in (you'll be
tested on these later): Sec 8.6: 1, 3, 23 (Hints: see formulas 60, 65, 42 in the book's tables of integrals.) Then redo the above problems using Mathematica. Do you get the same results? |
15 | F 3/7 | Review class notes on "Improper integrals using comparison". Also, carefully read (but don't have to do) problem 46. | Sec 8.8: 25, 27, 33, 41,
42, 47, 48, 50, 52, 62. Hint for 42: three ways to do this: 1. Let u = ln(x), dv = 1/x^2. 2. Do the substitution u = 1/x; it'll give you problem 41. 3. Substitute u = ln(x); after the substitution, continue by using integration by parts. Also do the following Extra Problem: (a) Find limit of x^x as x --> 0+. (b) Find (x^x)'. Hint: use the same trick as in part (a): x^x = e^ln(x^x). Solutions |
Mid 2 with solutions | W 3/5 | Covers HWs
8-13. Start reviewing a week in advance. |
Do not turn in; these are
optional, just for extra practice (and they do not necessarily cover
all topics covered by Midterm 2): Chapter 7 review exercises: 3, 6abcfg, 8, 11, 12a, 20. Chapter 8 review exercises: 11, 12, 47, 49, 50, Solutions |
14 | M 3/3 | Sec 4.4, especially pages 260-2. | Sec 4.4: 9, 15, 17, 21, 23, 25,
35, 39, 40, 49, 50, 51. Solutions |
13 | F 2/29 | Sec 8.8. Skip subsection "Arc length and surface area using improper integrals." | Sec 8.8: 3, 7, 9, 11, 13, 15. Also turn in all of the following problems. You need to learn them well in order to understand Friday's lesson. Arithmetic with large and small numbers Solutions ; Solutions to Arithmetic with large and small numbers |
12 | W 2/27 | Sec 8.7 pages 556-562; may skip
Error Bounds. Sec 8.8. Skip subsection "Arc length and surface area using improper integrals." Solutions to the first midterm are posted below (click on Mid 1). |
Sec
8.7: 27, 30a, 35,
37, 42. 27: Calculator OK except for finding the exact value of the definite integral. 30: 35, 37, 42: Calculator OK. Also turn in the lab problem (see below). Solutions |
lab | T 2/26 | Turn in this problem
with HW #12. No need to
print out results from the computer; just copy the final numerical
results by hand. Here's a brief intro to Mathematica. |
|
11 | F 2/22 | Read Sec 8.2; skip the subsection "A Tabular Method for ..."; the subsection "Reduction Formulas" won't be on exams either, but you may benefit from taking a brief look at it anyway. | Sec 8.2: 1, 7,
15-27(odds), 33, 34, 48. Solutions |
10 | W 2/20 | Sec 7.4: p. 465-466. Sec 7.6. |
Sec 7.6: 1, 14, 15, 17, 18, 19, 20, 29, 32. May use a calculator or a spreadsheet for problems 15, 32. Note: problem 32 is asking for average mass, not average rate. Read the problem carefully a few times before trying to solve it. The solution isn't very long, but it requires careful thinking. Sec 7.4: No problems to do, but you should be able to explain, like we did in class, or as done on page 466, how the formula for arc length (Definition 7.4.2) is obtained. Solutions |
lab | T 2/19 Canceled |
Canceled | |
9 | F 2/15 | Sec 7.2. | Sec 7.2: 1, 2, 3, 4, 5,
7, 25, 28, 34, 35. Solutions |
Mid 1 | Midterm 1 covers HWs
1-7 and
their corresponding sections. The exam problems will be similar to HW problems. Start reviewing all homework problems a week in advance; test yourself to see if you can do every problem without looking at solutions or the book. |
Optional (just for practice)
--- do not turn in: Chapter 6 review exercises: 9, 11a, 13-15, 17-20, 26, 33, 34, 36, 37, 54, 55, 76, 79, 80, 83, 86, 89. Note: These problems do not cover all the topics we covered in class (e.g., there are no problems on finding the area between two curves in these exercises). These problems are just for extra practice and for you to test your readiness; but the HW problems are the best indicator of the types of problems you will see on the test. |
|
8 | M 2/11 | Sec 7.1. | Sec 7.1: 1, 3, 5, 6, 7,
9, 15, 17, 41, 42. Solutions |
7 | F 2/8 | Sec 6.7 (all of it). Sec 6.8. |
Sec 6.7: 4, 15, 35.
(The figure for problem 4 is below it, not above it. It says Fig Ex-4). Sec 6.8: 9, 13, 40, 41, 52, 53, 54-56. Solutions |
6 | W 2/6 | Sec 6.6 pages 403-406 (skip
proof of Theorem 6.6.3). Sec 6.7 pages 410-412. |
Sec 6.6: 32, 35, 37,
51-59(odds), 71, 72, 73, 74. Do problems 35 and 37 in lab on Tuesday using a spreadsheet. Solutions |
5 | M 2/4 | Sec 6.5: Read p. 389-392; skim p. 386-388. May skip
Definition 6.5.7 and Theorem 6.5.8. Sec 6.6: p. 396-401. |
Sec 6.5: 15, 17, 19, 21, 27. Sec 6.6: 1, 5, 13, 17, 21, 29, 31, 49. Solutions |
4 | F 2/1 | Sec 6.4. Theorem 6.4.2: memorize part (a) only. May skip Theorem 6.4.4 and "Net Signed Area". | Sec 6.4: 1def, 5, 7, 17, 22, 23, 25, 29a, 33, 37. For problem 37, you must use a spreadsheet (Excel). Here's a brief Excel tutorial, if you need one. You can get help on this (and other problems) in lab on Tuesday. No need to turn in #37; but there will eventually be a quiz in lab on spreadsheets, so learn this problem well. Solutions |
3 | W 1/30 | Sec 6.3. | Sec 6.3: 1(ab), 9, 13, 17, 19, 21, 39, 42, 44, 45,
57, 61, 63, 69, 70. (Because this is a somewhat long assignment, we will do problems 1 and 3 of sec 6.3 in lab later -- in a week or two.) Solutions |
2 | M 1/28 | Sec 6.2; may skip "Integral Curves". | Sec 6.2: 1, 2, 9, 11, 17, 19, 27,
33, 41, 45, 66. Solutions |
1 | F 1/25 | Sec 6.1. | Sec 6.1: 1, 3, 21, 22, 23, 25. For problems 1 and 3, use n=2 and n=5 only, without a calculator; then use the Fundamental Theorem of Calculus (the "antiderivative method") to find the exact areas. On Tuesday, you will redo these two problems in lab for larger values of n, using a spreadsheet (details will be posted later). Solutions |