Math 231, Spring 2007. Class Diary:
Wednesday, 1/17: Introductions. The first assignment (HW1) is to read
Chapters 1--6 and write down two or three things you are uncomfortable or
unfamiliar with.
Friday, 1/19: Did a bunch of examples illustrating the use of
substitution and integration by parts techniques for evaluating indefinite integrals.
HW2, due Monday: Read § 7.1--7.3, peruse 7.4. Problems: §7.2; 9, 10, 13, 18, 33, 34; §7.3; 1, 2, 5, 6, 11, 14, 31, 32
Monday, 1/22: Recapped integration by parts, and talked about the
various places where it can be used. Started to talk about how one uses
trig identities to evaluate certain integrals.
HW3, due Friday: Read § 7.4, peruse 7.5. Problems: §7.3; 25,
30, 51, 52; §7.4; 1, 2, 11, 15, 16, 18.
Wednesday, 1/24: Finished the discussion of integrals involving trig functions. Did lots of examples. Talked about complex numbers.
First Honors Questions HQ1 due Wednesday 1/31.
HW4, due Monday: Read § 7.5. Problems: §7.3; 21, 28; §7.4; 4, 7, 19, 20, 43, 44; § 7.5; 1--6.
Friday, 1/26: Finshed the discussion of complex numbers (for now).
Started talking about the method of partial fractions for integrating
rational functions. Described the method in the special case that the
denominator has distinct linear factors. No new homework.
Another Hint for HQ1 If A and B are any two numbers, then |A+B| ≤ |A| + |B|. This is called the triangle inequality.
Monday, 1/29: Continued the discussion of partial fractions. Dealt with the next level of difficulty: possibly nondistinct linear factors in the denominator. Mentioned the general case---both linear and irreducible quadratic factors in the denominator.
HW5, due Friday 2/2: Read § 7.5 again. Problems: § 7.5; 8, 12,
13,
14, 25, 36, 38, 39.
Wednesday, 1/31: Discussed the honors question. Finished the
discussion of partial fractions.
HW6, due Monday 2/5: Read § 7.6, 7.7. Problems: § 7.5; 19, 20;
§ 7.6; 1--6, 9, 10, 13, 14, 22, 23, 31, 32, 46, 47, 50.
Friday, 2/2: Discussed method of trig substitution.
HW7, due Wednesday 2/7: Problems: § 7.7; 1--4, 7, 8, 15, 16, 21,
28.
HQ2: Here is the second honors question. It will be due, with the midterm, on Wednesday 2/14, and will count toward the exam. Do not talk to others, and do not consult the internet. You are to solve this problem using only your book, notes, and brain.
Monday, 2/5: Discussed the use of completing the square to evaluate integrals.
HW8, due Friday 2/9: Read § 7.8. Problems § 7.8; 1--6, 17, 18,
21, 22, 39, 40. Do all problems, but only turn in first eight (1--6, 17,
18) on Friday.
Wednesday, 2/7: Talked about Section 7.8.
Summary/Review for the first midterm. Don't forget to bring your honors question HQ2 with you to turn in during the exam!!!!!!!!!!!
Friday, 2/9: Oops, I never filled the activities of this day in. I think we finished the discussion of 7.8...
Monday, 2/12: Review day.
A word on HQ2: Some have asked what sort of answer I'm looking for
on HQ2. I'm expecting something like this: "When m and n are of the form
[blank], we can do a substituion [blank] to change the integral into
[blank], which is an integral of type [blank] and we know how to solve by
section [blank]." And you should exhaust all possibilities for m and n
with such methods. Hope that helps.
Wednesday, 2/14: class canceled
Friday, 2/16: Midterm 1.
HQ3, due Wednesday 2/21. § 7.7 problem 48.
This was supposed to be § 7.8. Turn in the problem from either
section.
Monday, 2/19: Started discussing sequences.
HW9, due Friday 2/23: Read § 10.1--10.3. Problems § 10.2; 5, 8, 9, 10, 27, 28, 39, 40, 57, 58; § 10.3; 11--14, 19, 20.
Wednesday, 2/21 Went over the exam very briefly. Got side-tracked
talking about sequences. No new homework assigned.
Friday, 2/23 Discussed § 10.3.
HW10, due Wednesday 2/28. § 10.3; 25, 26, 45, 46. §
10.4; 11--14, 21--24, 31, 32
HQ4, due Wednesday 2/28. § 10.2, problem 63. This explains the construction of the square root of two. More precisely:
In this problem you are constructing the square root of 2. You are not
supposed to assume that you know what the square root of 2 is. This
number is thus built from a bounded monotonic sequence of RATIONAL numbers
a_n (these are integral multiples of 1/10^n, and hence rational) from The
Bounded Monotone Sequence Property. Part (a) constructs the limit of a_n
and parts (b),(c), and (d) prove that the limit is indeed the square root
of 2---that is, the limit is a number which squares to 2.
Monday, 2/26 Discussed Taylor polynomials and Taylor series, §
10.4.
HW11, due Friday 3/2. Read 10.4 (again?) and 10.5. Problems: §
10.4; 19, 20; § 10.5; 1, 2, 5, 6, 13--16, 21--24.
I'll be gone Wednesday afternoon until the weekend. Prof. Rotman will teach class on Friday. Thursday's office hours are cancelled and rescheduled for tomorrow 10--11:50.
Also notice on the main page for the course, that we have now set a date for the second midterm. You'll recall at the beginning of the semester I asked whether you wanted it before or after the break... you said before, so there it is: March 16.
Wednesday, 2/28 Discussed integral test, § 10.5.
Friday, 3/2 Prof. Rotman discussed the comparison tests, §
10.6.
HW12: Read 10.6 and 10.7. Problems due Wednesday 3/7; §
10.5; 27, 28,
35, 36; § 10.6; 1--6, 15--18, 23, 24, 29--32.
Monday, 3/5 Discuss absolute convergence, ratio and root
tests, § 10.7.
HW13: Read 10.7 (again), 10.8. Problems due Friday
3/9; § 10.7; 9--18, 21, 22, 25, 26, 31--34.
Wednesday, 3/7 Review all the tests for convergence and do lots of
examples. Discussed alternating series test and proofs of ratio test and
alternating series test. Handout on
Tests for series. Read 10.8 and 10.9!!
Thursday, 3/8 "Introducing... THE REAL NUMBERS!!". We'll meet in
my office around 3:30 and talk about the real numbers. I'll explain what they really are....
Friday, 3/9 Power series.
HW14: Read 10.8 (again), 10.9. Problems due Monday 3/12; § 10.8;
1--12, 17, 20--26, 31--36, 41, 42. § 10.9; 23 -- 26.
Just turn
in problems 1--12, 17, and 20--26 from § 10.8, but do all the
problems!
Partial
review sheet for midterm 2
Monday, 3/12 Finish the discussion of Power series. Review and
discuss.
A helpful site: John Endicot noticed the following
website,
which contains some helpful discussion of sequences and series. Take a
look, it might just help you ace the exam!!
Wednesday, 3/14 Review and discuss.
Extra Credit for exam. 3 points.
Thursday 3/15 Extended office hours, 8:30--11:50.
Problems If you want extra practice for the exam, go to the end of
the chapter and work on the problems there. There's a set of problems
deciding convergence or divergence. These are good ones to work on (if
you find convergence, then you should also decide whether it is absolute
or conditional). There's another set (I think) on radius of convergence.
These are also good to do.
Friday, 3/16 Midterm 2.
Monday, 3/26 Returned Midterm 2. Started § 6.4.
HW15: Read § 6.4 and § 9.1. Problems due Friday 3/30: §
6.4; 4, 5, 8, 9, 11, 12, 16, 17, 21, 22, 29, 30; § 9.1; 1, 4, 8, 9,
11, 12, 17, 18, 25, 26.
Wendnesday, 3/28 Finished § 6.4. Talked about analytic
geometry and § 9.1.
Friday, 3/30 Prof. Rotman covered § 9.2. Let me know (by
email) if you want me to talk about § 9.2 anymore. If not, I'll
start on § 9.3 on Monday.
HW16: Read §: 9.2 and § 9.3. Problems due Wednesday 4/4 §
9.2: 1, 2, 5, 6, 13, 14, 22, 23, 33, 34, 53, 54.
Monday, 4/2 Did some more examples from § 9.2. Started the
discussion of § 9.3.
HW17: Read § 9.3-- 9.5. Problems due Friday 4/6 § 9.3:
10, 11, 12, 17, 18.
Wednesday, 4/4 Finished the discussion of § 9.3, but will take
5 minutes to clarify the last example next time.
HW18: Read § 9.4--9.5. Problems due Monday 4/9 § 9.3: 25, 26, 32, 33, 38. § 9.4: 1, 2, 3, 4.
Regarding midterm 3. We will keep it on Friday 4/27. It will cover 6.4,
8.1, and 9.1--9.6.
Office hours on Thursday, 4/5 are shifted to 9:00--10:50.
HQ5. Here is honors question 5. I hope its fun. It's due Friday the 13th...spooky.
Friday, 4/6 I ended up talking more about loci of polar equations. Then I talked about complex numbers and multiplication again (now that we have the apprpriate "tools": power series and polar coordinates). I finished with a brief introduction to parameterized curves and eliminating the parameter from § 9.4.
Monday, 4/9 We started a proper discussion of parameterized
curves. We eliminated the parameter in several examples, and found
parameterizations for some geometric/physical paths of motion.
HW19: Reread § 9.4--9.5. Problems due Friday 4/13 § 9.4: 15, 16, 21, 22, 25, 26, 30, 34.
Hint for HQ5:
Q: What does the equation x + iy = 1 mean?
Q: x = 1 and y = 0.
Wednesday, 4/11 Talked about parameterized curves more.
Specifically: tangent lines, how to think of polar curves as parameterized
curves, and tangent lines to polar curves.
Read § 11.1.
Friday, 4/13 Talked about tangent vectors, speed, and arc
length.
HW20, due Wednesday 4/18 UPDATED!: § 9.5: 1, 2, 5, 6, 11--14, 19, 20.
Monday, 4/16 Covered § 9.5.
Wednesday, 4/18 Started discussing § 9.6 on conic sections. Covering parabolas and ellipses in detail and mentioned hyperbolas.
HW 21, due Friday 4/20: § 9.6: 6, 7, 19, 20, 39, 40.
Friday, 4/20 Finished the discussion of conic sections. Talked about hyperbolas and then discussed some cool facts about ellipses.
Review for midterm 3 is Here.
Note that § 8.1 will not be on midterm 3 (though it will be
covered on the final exam).
Monday, 4/23 Cover § 8.1.
HW 22, not due (even solutions will be posted next week): § 8.1: 1, 2, 4, 5, 7, 8, 21, 22, 29, 30, 33, 34.
Office hours this week moved: All morning Tuesday (8:30--12:00).
Wednesday, 4/25 Review for midterm 3. Evaluations.
Friday, 4/27 Midterm 3.
Monday, 4/30 Return midterm 3.
Tuesday, 5/1 Thursday's office hours are rescheduled for 5/1
9--11.
Wednesday, 5/2 Last day of class!! Review for final exam.
Monday, 5/7 Office hours all day long.
2 points Extra credit (for final exam): Find a clever/slick/elegant/... proof of the equation (14) on page 651 of your text. This is due on or before the beginning of the final exam.
a few solutions to the even problems from § 8.1 here
Tuesday, 5/8 Final Exam, 8:00am to 11:00am. In the usual room, Altgeld 145.
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