Table of topics and assignments - Calculus II - Spring 2014
You may buy the textbook, Calculus, by H. Anton and others, Early Transcendentals, 10th edition, directly from the publisher following this link. Since it is only $5 more, I would advise you to get the complete version of the text, (Chapters 1-15) which includes the multivariable part done in Calculus III. The WileyPLUS is an online homework system that you may find useful, but I will not require it this semester.
For tutoring services (including online) and other useful info follow this link . There you will also find a link for the complete solution manual. This requires username and password which I'll give in class.
Learning Assistants: Agnes
Arrinda [aarri020"at"fiu.edu] and
Brandon
Mori
[bmori006"at"fiu.edu]
The structure of the exams will be roughly as follows: about 80% is at the level of standard suggested problems and 20% at the level of more difficult suggested problems or theoretical topics (proofs that you will be asked to know). There is always a 10% bonus which may test your creativity and capacity to reason. In the suggested assignment below, the more challenging problems are denoted with a star. You should do enough of the suggested problems to be sure you understand the technique and/or idea behind them. If you have troubles with the suggested problems, particularly the standard ones, be sure to ask for help (my office hours, the tutoring services, colleagues, the LAs).
You may find useful the free version of the WolframAlpha computer software system . You can use this system at home to check your work, but it is essential that you are able to do computations on your own, not just rely on the software package. For your exams you will not be allowed any kind of electronic devices.
You may also find useful the following videos delivered by Professor David Jerrison, MIT.
| Date | Topics covered | Suggested Assignment | Comments |
| Jan. 7 | 5.4 Area as limit; Sigma notation | 1-19odd, 10, 21-23all, 35, 37, 41, 43, 51, 53, 57-61all |
Read also section 5.1. Proof of Theorem 5.4.2 parts (a) or (b) could be a possible theoretical exam topic. See your notes. |
| Jan. 8 | Pb. session 1 |
Worksheet 1 | |
| Jan. 9 |
5.5 The Definite Integral |
9-29odd, 37, 41 |
Chapter 5 from our text corresponds roughly to
sessions 43-56 from the MIT course (see link
above) Quiz 1 on Thursday, Jan. 16, covers 5.4, 5.5, 5.6. |
| Jan. 14 | 5.6 Fundam. Thm. of Calculus | 1-39odd, 45-51odd, 55-63odd, 69, 70, 72* | Possible theoretical exam topic: Proof of Thm. 5.6.3 (FTC). See text or your notes. |
| Jan. 15 | Pb. session 2 | Worksheet 2 | |
| Jan. 16 |
5.7 Rectilinear motion 5.8 Average value of a function Quiz 1 |
1, 4, 11, 14, 31-43 odd 1-11odd, 15-28all |
Quiz 1 shows that many of
you need to review ASAP (this weekend) basic
anti-derivatives (section 5.2). As is related to 5.9 and will be one the most used computational technique through the course, please also review the substitution method for indefinite integrals (section 5.3). |
| Jan. 21 |
5.9 Substitution Method |
1-47odd, 54*, 63*, 65* 15, 17, 24*, 25, 28*, 31, 43 |
For 5.2 and 5.3 these
were my suggested pbs in Calculus 1: 5.2. 1,11-25odd,33,43,45,53 5.3. 1,3,5,15-59odd,71,76,77* |
| Jan. 22 | Pb. session 3 | Worksheet 3 | Quiz 2 on Thursday Jan. 23 covers sections 5.8, 5.9 (no motion pbs on this quiz) |
| Jan. 23 |
5.10 Logs & other functions Quiz 2 |
15, 17, 25, 28*, 29, 31, 39, 43 |
|
| Jan. 28 |
6.1 Area between curves 6.2 Volumes by slicing |
1-9odd, 11-14all, 35, 36 1-15odd, 19, 23, 25, 39-42all, 49*, 50*, 60* |
|
| Jan. 29 | Pb. session 4 | Worksheet 4 | |
| Jan. 30 | 6.3 Vol. by cyl. shells | 1-4all, 5-15odd, 27-29all, 34* |
Exam 1 on Thursday, Feb. 6. Please note the
different date compared to syllabus. It covers all sections done up to and including 6.3 (but not 6.4, 6.5). |
| Feb. 4 |
6.4 Arclength |
3-5all, 27-31odd (do these after Exam 1) |
One problem on Exam 1 will
be one of the following proofs: Theorem 5.4.2 parts (a) or (b); FTC part (b) (assuming MVT for integrals); FTC part (a) (assuming part (b)); deriving equations (10), (11) in 5.7.2 (motion with constant acceleration); deriving the volume formulas for a pyramid or cone (with arbitrary base). |
| Feb. 5 | Pb. session 5 |
Review for Exam 1 From Chap. 5 Review Exercises: 11, 12, 19-21, 26-29, 30*, 31-41odd, 49-53odd,61-65all, 67-77odd, 80-88all, 90* |
Searching my website -- see the previously
taught courses link on my main page -- you'll
find exams given in past semesters. Working on past exams is helpful, but the ideal practice is to solve all of the suggested homework problems. Each such problem may be an exam question. |
| Feb. 6 | Exam 1 | Solution key of Exam 1 | For last problem (FTC) see your notes or the text. |
| Feb. 11 |
6.9 Hyp. Trig.& Cables 6.5 Surface Area |
Example 4 + Pbs. 70,71,72 1-7odd, 23, 26*, 27*, 33, 36, 37 |
|
| Feb. 12 | Pb. session 6 | Worksheet 6 | Homework due Wednesday, Feb. 19: Pbs 2 and 3 on Worksheet 6 |
| Feb. 13 | 6.6 Work | 7-9all, 14-19all, 21, 22, 24, 25 | |
| Feb. 18 |
7.1 More int. by substitution 7.2 Integration by Parts |
1-15odd, 24, 25, 28, 29 1-29odd, 55, 57, 60*, 61a, 62b, 63*, 64*, 68* |
|
| Feb. 19 | Pb. session 7 | Worksheet 7 | |
| Feb. 20 |
7.3 Trigonometric integrals 7.4 Trig. subs |
1-11odd, 17, 25, 29, 33, 39, 40, 68*, 70* 1-29 odd, 31-35 all, 37, 39 |
|
| Feb. 25 | 7.5 Partial fractions | 1-8 all, 9-33 odd, 49, 50 | Exam 2
on Tuesday, Mar. 4, covers all sections done
from 6.4 to 7.5 (including these). Possible theoretical topics for Exam 2: proof of IBP, proof of the kinetic energy/work relation, derivation of a reduction formula. |
| Feb. 26 | Pb. session 8 | Worksheet 8 | Searching my website -- see
the previously taught courses link on my main
page -- you'll find past exams. These are helpful, but the ideal practice is to solve all of the suggested homework problems. Each such problem may be an exam question. |
| Feb. 27 |
7.8 Improper Integrals Review for Exam 2 |
1, 2, 3-39 odd, 45-51 odd, 55 (do these after Exam 2) |
Extra office hours:
Monday, Mar. 3, 11-12noon, 1-2:30pm |
| Mar. 4 | Exam 2 | Solution key to exam 2 | Reminder of LAs hours (outside DM 409A) Agnes -- Fridays 10am-12noon Brandon -- Mondays 4-6pm |
| Mar. 5 | Pb. session 9 | Spring Break Homework | This is due on Wed. Mar. 19 |
| Mar. 6 |
10.2 Polar Coords. |
3, 6, 9, 11, 17-49 odd |
|
| Mar. 11 | Spring Break | Enjoy your Spring Break! | |
| Mar. 12 | Spring Break | Your overall percentage so
far. I dropped the lowest of the 6 quizzes/worksheets. Recorded are the first 5 digits of your PID. |
If you overall percentage is below or around the 65%
passing line, you need to make a decision about staying in the class before the dropping date of Monday, March 17. |
| Mar. 13 | Spring Break | ||
| Mar. 18 | 10.3 Area in Polar coords | 25, 29-39 odd | |
| Mar. 19 | Pb. session 10 | Worksheet 10 | |
| Mar. 20 |
9.1 Sequences 9.2 Monotone seq |
1-4all, 5-29odd, 31-34all, 42*, 43, 46* 1-25odd, (27-31)* all |
Here is the solution of the Spring Break Homework for your review |
| Mar. 25 | 9.3 Def. of Series | 1-14all, 17-24all, 27-30all, 35-37all | |
| Mar. 26 | Pb. session 11 | Worksheet 11 | Pb. 1 parts (d), (e), (f) you can do for your own
pleasure! Here is a (fairly) complete solution of this worksheet. |
| Mar. 27 | 9.4 Div. test, Int. test, p-series | 1-8all, 9-25odd | |
| Apr. 1 |
9.5 Comp. & ratio tests 9.6 Alt. series; Abs. & cond. conv. |
1-4all, 5-15odd, 22, 23,25-49odd, 51*,54* 1-27 odd, 31,32*, 37, 39, 43, 48*,51*,52* |
|
| Apr. 2 | Pb. session 12 | Worksheet 12 | Worksheet 12 is a homework due Tuesday,
April 8. Here is a short answer key for Worksheet 12 . On a test, you'd be expected to give more details on Pbs 1 and 2 |
| Apr. 3 |
9.6 Alt. series; Abs. & cond. conv. 9.8 Power series, interval of conv. |
1-27 odd, 31,32*, 37, 39, 43, 48*,51*,52* 29-47 odd |
|
| Apr. 8 |
9.7 Taylor polys 9.8 Taylor series |
7-12all, 17, 21, 23 1-6all, 11-27odd |
Exam 3 on Tuesday April 15 covers sections
7.8, 10.2, 10.3 and 9.1 through 9.8. Possible theoretical topics on Exam 3 (you need to know the proofs of these): The area formula in polar coordinates (in the text, 10.3.4 formula (6), with the argument above), Theorem 9.3.3 (Geom. series thm.), Theorem 9.4.1 (k-th term div. test); Theorem 9.4.6 (series with non-neg. terms); Theorem 9.5.1 (simple comp. test). |
| Apr. 9 | Pb. session 13 | Worksheet 13 |
From Chap. 9 Review, these are good exercises for
Exam 3: 1-5all, 7-14all, 15-23all, 25, 26, 28, 29, 33* I have uploaded solutions for worksheets 11 and 12 (see above). |
| Apr. 10 |
9.9 Remainder estimate 9.10 Operations with Taylor series |
1, 3, 5, 9, 10 (do these after exam 3) 1, 2, 5, 6, 27, 28, 36*, 37, 40 (do these after exam 3) |
Extra office hours for Exam 3: Friday 12:00-2:00pm, Monday 11-12noon, 1-2:30pm |
| Apr. 15 | Exam 3 | Solution key for Exam 3 | |
| Apr. 16 | Pb. session 14 |
The final exam is comprehensive. Expect about 1/3 or maybe a bit more of the final to be from series. The rest will be on integration and its applications. One problem will be from polar coords. (likely an area pb for a polar curve). Expect also a problem with an error estimate (9.9) and something regarding operation with series (9.10). Review the three exams and the worksheets. If you have time to review section by section (this would be best), try to understand what are the central ideas in each section and do a couple of problems from each. |
Possible theoretical topics for final:
FTC part (b) (assuming MVT for integrals); FTC part (a) (assuming part (b)); proof of IBP; The area formula in polar coordinates (in the text, 10.3.4 formula (6), with the argument above); Theorem 9.3.3 (Geom. series thm.); Theorem 9.4.1 (k-th term div. test); |
| Apr. 17 | Review for Final | Here is the final exam given
last semester for your practice. As usual, your exam exam may be quite different. Here is the solution key for the final of last semester. |
Office hours for the final: Friday, April 18, 3-5pm, Monday, Apr. 21, 9:30am-2:30pm |
| Apr. 22 | Final Exam | 9:45-11:45am, EC 2440 Solution key for the final. |
|
| These are your
scores and grades. 1st column - first 5 digits of your Panther ID 2nd column - score on the Final Exam (out of 150 pts) 3rd column - total on quizzes&worksheets (out of 100 pts) (lowest 2 scores were dropped) last column -- your grade in the class. |
Have a good Summer! | ||