This page gives information about the material covered each day in the MATH 107 recitation, as well as assigned homework problems.
Handed out the recitation information sheet (PDF, TeX). Discussed Section 5.4. The first quiz will be on Friday, January 12; it will cover Sections 5.4 and 5.5.
Recommended homework problems (these will not be graded):
Discussed Sections 5.4 and 5.5. Took the first quiz (PDF, TeX). Solutions are available (PDF, TeX). Quiz grades have been posted on Blackboard.
Handed back Quiz 1; solutions are available (PDF, TeX). Talked about the substitution method, and then moved on to Section 7.1, integration by parts. The quiz this week will likely cover Sections 7.1 and 7.2.
Discussed the method used to evaluate integrals that look like ∫ ex sin x dx or ∫ ex cos x dx. (See Example 4 in Section 7.1.)
Also talked about one method used to evaluate integrals that look like ∫ sinm x cosn x dx, which works if either m or n is odd. (See Examples 1 and 2 in Section 7.2.)
Took the second quiz (PDF, TeX). Solutions are available (PDF, TeX).
Recommended homework problems (these will not be graded):
These homework problems cover the other trigonometric methods described in Section 7.2. Understand how to do these problems. If you have any questions, please let me know. I probably won't be able to cover these methods explicitly in recitation, due to time constraints, but they may appear on an exam. On Wednesday I may assign some problems like these as graded homework.
I have exchanged my Tuesday and Thursday office hours, so that my office hours are now 1:30 to 3:00 on Tuesdays and 2:30 to 4:30 on Thursdays. Of course, you can always contact me to set up an appointment to meet at another time.
Worked through a couple of examples from Sections 7.2 and 7.3.
Assigned problems 21, 29, and 37 from Section 7.2 as homework. These problems will be graded. They are due by the end of the recitation on Friday, and will count for nine of your 15 points for this week.
It was asked in the recitation today whether I would allow note cards for quizzes. This seems fine to me, so you may bring one 3″ × 5″ note card each Friday for the quiz.
Worked an example of integrating a rational function by using the method of partial fractions (Section 7.4). We also did one quick example from Section 7.3. The third quiz (PDF, TeX) covered Sections 7.3 and 7.4. Solutions for the third quiz are available (PDF, TeX) as are solutions for the first set of homework problems (PDF, TeX).
Talked briefly about Section 7.5, Integral Tables and Computer Algebra Systems, and worked one example illustrating how to use tables of integrals. We then discussed the trapezoidal rule and Simpson's rule from Section 7.6, did Problem 4 from that section, and used the error estimate formulas on page 481 to find the maximum error in our answers.
Homework this week is problems 14, 22, and 30 from Section 7.5. These problems will be graded. They are due by the end of the recitation on Friday, and will count for nine of your 15 points for this week.
The quiz on Friday will cover Sections 7.6 and 7.7. Remember that you may bring one 3″ × 5″ note card for the quiz if you like.
Talked about improper integrals, and worked an example problem. Gave the fourth quiz (PDF, TeX).
Answered some questions about the trapezoidal rule and Simpson's rule. Handed out a sheet containing problems for two practice gateway exams (PDF, TeX).
Very quickly worked the seventh problem on the first practice gateway exam, and then gave the actual gateway.
Reviewed for the first exam, which will be given on Friday. Discussed a problem from Section 6.6, Work, and went into a little bit of detail about what negative work means. Also talked about exponential change and did a couple of problems from Section 6.5.
Exam.
Began talking about sequences and series (Chapter 8), and what it means for a sequence or a series to converge or diverge.
Talked about several tests for convergence of a series, including the nth-term test, the p-series test, and the integral test. Gave the fifth quiz (PDF, TeX).
Discussed the problems on Quiz 5 and talked about logarithms for a bit. This week there will be no quiz; instead, I have assigned the following problems, which will be due on Wednesday, March 7.
My office hours on Thursday, March 1 will be canceled due to a dentist appointment. My office hours for Tuesday, March 6 will happen as usual. If you have questions between now and Tuesday, you can ask them in recitation on Friday or send me an e-mail. You can also go to the Math Resource Center in Avery Hall 13B for help. The MRC is open on Mondays, Tuesdays, Wednesdays, and Thursdays from 12:30 to 8:30 p.m.; on Fridays from 12:30 to 2:30 p.m.; and on Sundays from 1:00 to 5:00 p.m.