Math 230, Spring 2006. Class Diary:
Wednesday, 1/18: Introductions. The first assignment is to read Chapters 1--6 and write down two or three things you are uncomfortable or unfamiliar with.
Friday, 1/20: Did a bunch of examples illustrating the use of substitution and integration by parts techniques for evaluating indefinite integrals. HW2, due Monday: §7.2-- 9, 10, 13, 18, 33, 34; §7.3-- 1, 2, 5, 6, 11, 14, 31, 32
Monday, 1/23: Reviewed Riemann sums and the fundamental theorem of calculus. Did more examples illustrating integration by parts. Talked briefly about complex numbers and trig. identities. HW3, due Friday: §7.3-- 25, 30, 51, 52; §7.4-- 1, 2, 11, 15, 16, 18
Wednesday, 1/25: Reviewed complex numbers briefly and trig identities. Talked about trig substitution and worked out some examples. Honors Question 1 is due Wednesday 2/1.Solution No other homework assigned.
Friday, 1/27: Finished the discussion of trig. integrals and started talking about how to integrate rational functions; heading toward the method of partial fractions. HW4, due Wednesday: §7.3-- 21, 28; §7.4-- 4, 7, 19, 20, 43, 44; §7.5-- 1--6.
Monday, 1/30: Talked more about partial fractions, and did a bunch of examples. HW5, due Friday: §7.5-- 8, 12, 13,
14, 25, 36, 38, 39.
Notes on honors question 1
When describing the negative of a complex number Z =x+iy, I should have said
-Z = -x + i(-y)
In the first part of (b), writing Z = x+iy, I want you to express 1/Z in the form u+iv,
where u and v are each expressions in
terms of x and y. For the second part, I want 1/Z in terms of Z and Z as
sums/products/differences/and quotients of Z and Z without any
complex numbers in the denominator.
When I say the "Complex plane", I'm referring to the identification of the
complex numbers with the Cartesian plane where we identify the complex
number x+iy with the point (x,y).
When I say "express x and y in terms of square roots", I should have said "express x and y in terms of numbers, and possibly some square roots"
Wednesday, 2/1: Finished up partial fractions (finally) and did some lengthy example. Also started on trig. substitution to complete the example. HW6, due Monday: §7.5-- 19, 20; §7.6-- 1--6, 9, 10, 13, 14, 22, 23.
Friday, 2/3: I fumbled through a couple more trig. substitution examples at the board. HW7, also due Monday: §7.6-- 17, 18, 31, 32, 46, 47, 50; §7.7-- 1,2. Honors Question 2 is due Friday 2/10.
Monday, 2/6: We finished the discussion of how completing the square can be useful in evaluating certain integrals involving quadratic polynomials. We ended with a review of the various techniques of integration. HW8, due Friday 2/10: §7.7-- 3, 4, 7, 8, 15, 16, 21, 28; Honors Question 3: §7.7 problem 48 is due Monday 2/13.
Wednesday, 2/8: Started talking about indefinite integrals. HW9,
also due Friday 2/10, first 8 problems only: §7.8-- 1--6, 17, 18,
21, 22, 39, 40.
Friday, 2/10: Finished the discussion of indefinite intergrals, did some examples, talked about a weird (or wired) thing: Gabriells horn, and spent time talking about the Gamma function. HW, not to be turned in but you better do it: §7.8-- 53, 60, 61.
I never did confirm a room for the questions session on Sunday
afternoon/evening 4:00--6:00. Let's just meet in our usual classroom and
work there if possible. If not, then we'll post a sign saying where we're
going. Remember also that you can come to my office anytime Monday
morning to ask questions, say between 8:30 and class time 11:00. I'll
also be answering questions on Monday in class.
Monday, 2/13: Answered questions.
Wednesday, 2/15: Exam 1.
Friday, 2/17: No class.
Monday, 2/20: Started discussing infinite sequences. Gave some examples and an in-depth discussion of convergence. HW10, due Friday 2/24: §10.2-- 5, 8, 9, 10, 27, 28, 39, 40, 57, 58; §10.3-- 11--14, 19, 20.
Wednesday, 2/22: Finished the discussion of sequences and convergence.Honors Question 4 is due Friday 3/3.
Friday, 2/24: Started and finished §10.3. HW11, due Wednesday 3/1: §10.3-- 25, 26, 45, 46; §10.4-- 11--14, 21--24, 31, 32.
Monday, 2/27: Started and mostly finished §10.4 on Taylor polynomials, remainders, and Taylor series. We'll finish next time. HW12, due Friday 3/3: §10.4-- 19, 20; §10.5-- 1, 2, 5, 6, 13--16, 21--24 (only need to turn in even problems, but do them all!!
Wednesday, 3/1: Finished §10.4 and §10.5 on the integral test. It's essentially the same thing we did to show that the series Σ 1/n diverges. Just reiterated the homework I meant to assign last time, but forgot to do.
Friday, 3/3: Discussion of the comparison test and limit comparison test. Here are the next two homework assignments:
HW13 due Wednesday 3/8: §10.5-- 27, 28, 35, 36; §10.6-- 1--6, 15--18, 23, 24, 29--32.
HW14 due Friday 3/10: §10.7-- 9--18, 21, 22, 25, 26, 31--34.
I'll be gone next monday, but Prof. Kerman will be covering the class. I'll be back on Wednesday.
Wednesday, 3/8: Breifly recalled tests for convergence and divergence, discussed absolute convergence, then introduced the last two tests: the ratio and root tests.
Friday, 3/10: Started talking about power series. Defined radius of convergence and proved absolute convergence on the open interval and divergence on the open rays in the complement.
HW15 due next Wednesday 3/15 § 10.8-- 1--12, 17, 20--26, 31--36, 41, 42.
HW16 You can turn it in next Friday 3/17 or Monday after break 3/27 §10.8-- 49--52; §10.9-- 23--26.
I'll be gone next Friday 3/17, no class. Put HW16 in my mailbox if you turn it in on Friday.
Monday, 3/13: Continued talking about power series. Revisited ratio and root test to determine radius of convergence. Gave some examples. Also discussed differentiation and integration.
Wednesday, 3/15: Finished the discussion of power series.
Monday, 3/27: Went over some homework problems and answered questions. Talked about rearrangements a little bit more. Don't forget, exam on Friday!!
Wednesday, 3/29: Reviewed for exam 2 and answered questions.
Friday, 3/31: Exam 2.
Monday, 4/3: Returned exam 2, went over solutions, discussed §6.4. HW17 due Friday 4/7 §6.4-- 4, 5, 8, 9, 11, 12, 16, 17, 21, 22, 29, 30; §8.1-- 1, 2, 4, 5, 7, 8, 21, 22, 29, 30, 33, 34.
Wednesday, 4/3: Finished the discussion of §6.4 and went over §8.1.
Friday, 4/5: Discussed §9.1. Messed up a sign at the end of class in the calculcation. I'll fix that next Wednesday. HW 18 due Monday 4/10 §9.1-- 1, 4, 8, 9, 11, 12, 17, 18, 25, 26.
Monday, 4/10: Prof. Nevins covered §9.2. HW 19 due Friday 4/14 §9.2-- 1, 2, 5, 6, 13, 14, 22, 23, 33, 34, 53, 54.
Wednesday, 4/12: Covered §9.3 on area of a region bounded by a polar curve. HW20 PART 1 due Wednesday 4/19 §9.3-- 10, 11, 12, 17, 18.
Friday, 4/14: Covered most of §9.4 on parametric curves. HW 20 PART 2due Wednesday 4/19 §9.4-- 1, 2, 3, 4, 15, 16, 17, 18, 30.
Monday, 4/17: Finished §9.4. Exam 3 has been moved to May 1!!!
Wednesday, 4/19: Prof. Tyson covered §9.5.
Friday, 4/21: Finished §9.5 and did some more examples. Last two homework assignments.
HW21 due Monday 4/24 §9.5-- 1, 2, 5, 6, 11, 12, 29, 30.
HW22 due Wednesday 4/26 §9.6-- 6, 7, 13, 14, 19, 20, 35, 36, 39, 40.
Monday, 4/24 Covered most of §9.6.
Wednesday, 4/26 Finished the discussion of §9.6.
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