# Record of daily activities, Math 152, Engineering Mathematics II, Honors Sections 819-820, Fall 2002

Monday, September 2
We looked at some motivating examples for studying calculus (the birdcage problem, understanding rainbows); we quickly reviewed the fundamental theorem of calculus stating that differentiation and integration are inverse operations; we observed that the method of integration by substitution is just the fundamental theorem combined with the chain rule for differentiation.
Homework for Wednesday: Do as many of the odd-numbered review problems (odd-numbered problems have answers in the back of the textbook) for Chapter 6 on pages 416-418 as you need to do to be confident that you would get them right on a quiz. If there are problems that you are puzzled about or that you don't know how to do, ask about them in class on Wednesday or in recitation on Thursday.
Wednesday, September 4
We discussed some of the problems in the Review section at the end of Chapter 6, pages 416-418.
Homework for Friday: Read section 7.1 and work the Suggested Homework problems for section 7.1 that are posted at the main Math 152 web site.
Friday, September 6
We discussed some illustrative examples of integration: in particular, how to compute the volume of the Great Pyramid of Cheops.
Homework for Monday: Read section 7.2 and work the Suggested Homework problems for section 7.2 that are posted at the main Math 152 web site.
Monday, September 9
We discussed various methods for finding the volume of a truncated pyramid. The formula for the volume can be interpreted as one-third the height times the sum of the following three quantities: the area of the base, the area of the top, and the geometric mean of those two areas. The same formula holds (by essentially the same calculation) for a truncated cone whose base has an arbitrary shape.
Homework for Wednesday: Read section 7.3 and work the Suggested Homework problems for section 7.3 that are posted at the main Math 152 web site.
Wednesday, September 11
We worked on various volume problems: number 18 on page 438 (both by washers and by shells); the donut (number 63 on page 439) both by washers and by shells; the birdcage (number 64 on page 439); and the napkin ring (number 42 on page 445).
Homework for Friday: In Problems Plus, pages 454-457, do numbers 1, 13, 15, and 18.
Friday, September 13
We discussed the homework problems.
Homework for Monday: In Problems Plus, pages 454-457, do numbers 3, 7, 19, and 25.
Monday, September 16
We discussed the method of integration by parts, including as examples problems 1, 18, and 44 on page 463 in section 8.1.
Homework for Wednesday: Read section 8.1 and work the Suggested Homework problems for section 8.1 that are posted at the main Math 152 web site.
Wednesday, September 18
We looked at problem 23 on page 456 (in Problems Plus for Chapter 7) from the point of view of average value and integration by parts.
Homework: Before recitation on Thursday, work the Suggested Homework problems for section 7.5 that are posted at the main Math 152 web site. Before class on Friday, read section 7.4.
Friday, September 20
I attended a conference in Princeton, so Professor Fulling substituted and covered section 7.4.
Homework for Monday: Work the Suggested Homework problems for section 7.4 that are posted at the main Math 152 web site.
Monday, September 23
We discussed integrating rational functions by the method of partial fractions.
Homework for Wednesday: Read section 8.4 and work problems 17, 19, 21, and 23 on page 485.
Wednesday, September 25
We continued the discussion of integrating rational functions by the method of partial fractions, with an aside on the fundamental theorem of algebra.
Homework for Friday: Read sections 8.2 and 8.3 and work problems 1, 3, and 5 on page 470 (section 8.2) and problems 3, 7, and 9 on page 476 (section 8.3).
Friday, September 27
The integration of rational functions led us to the problems of integration via trigonometric substitution and integration of powers and products of trigonometric functions.
Homework for Monday: Finish the Suggested Homework problems for sections 8.2 and 8.3 that are posted at the main Math 152 web site.
Monday, September 30
We discussed methods for numerical approximation of integrals, including the midpoint rule, the trapezoidal rule, and Simpson's rule. We also saw how integrating the linear approximation formula leads to an error bound for the midpoint rule.
Homework for Wednesday: Read section 8.8 and work problems 1, 5, 29, and 31 on pages 507-508.
Wednesday, October 2
We did some review problems in preparation for the upcoming examination on Wednesday, October 9, on Chapters 6, 7, and 8.
Friday, October 4
In preparation for the upcoming examination on Wednesday, October 9, on Chapters 6, 7, and 8, we looked at two sample problems.
Monday, October 7
We further discussed improper integrals.
Reminder: The first examination is Wednesday, October 9, at the usual meeting time in the usual room.
Wednesday, October 9
First examination
Friday, October 11
We discussed first-order linear ordinary differential equations.
Homework for Monday: Read section 9.2 and do problems 5, 9, 15, 17, 25, and 33 on pages 540-541.
Monday, October 14
Some discussion of the normal distribution accompanied the return of the graded examinations. Also we continued the discussion of first-order differential equations, including an example of a Bernoulli equation.
Homework for Wednesday: Read sections 9.1 and 9.3. Do problems 3, 5, 9, 17, and 35 on pages 533-535 in section 9.1, and problems 1 and 6 on page 573 in Problems Plus.
Wednesday, October 16
We discussed some homework problems (the logistic equation, slicing pizzas into equal-area portions, a sneaky substitution for integrating 1/(x^7-x)) and the length of curves.
Homework for Friday: Read section 9.4. In section 9.3, pages 546-547, do problems 3, 5, 7, 9, and 27. In Problems Plus, page 573, do problems 9 and 12.
Friday, October 18
We looked at examples of arc lengths and surface areas, including Gabriel's Horn.
Homework for Monday: Read sections 9.5 and 9.6. Do problems 1, 9, 11, 19, 23, and 27 on page 553 in section 9.4.
Monday, October 21
We looked at some problems from sections 9.5 and 9.6 in the textbook (centroids and hydrostatic force).
Homework for Wednesday: Do the Suggested Homework problems for sections 9.5 and 9.6 that are posted at the main Math 152 web site.
Wednesday, October 23
We discussed the notion of an infinite sequence and some examples of convergent sequences.
Homework for Friday: Read sections 10.1 and 10.2 and do problems 15, 19, 21, 23, 31, 43, 45, and 47 on page 585 in section 10.1.
Friday, October 25
After discussing the arithmetic-geometric mean (see also problem 47 on page 585 in section 10.1 in the textbook), we looked at some examples of infinite series, in particular the geometric series.
Homework for Monday: Do problems 11, 13, 19, 21, 27, 33, 43, 47, 53, and 55 on pages 593-595 in section 10.2.
Monday, October 28
We discussed the Cantor set (see problem 53 on page 594 in section 10.2 of the textbook) from the point of view of geometric series, and we looked at approximating the sum of the series 1/n(ln(n)^2) by integrals (see problem 28 on page 604 in section 10.3 of the textbook).
Homework for Wednesday: Read section 10.3. Do problems 1, 3, 5, 7, 9, 11, and 31 on pages 603-604 in section 10.3, and problem 5 on page 649 in Problems Plus (about the snowflake curve).
Wednesday, October 30
We discussed comparison tests for convergence/divergence of infinite series, including (not in the textbook) the Cauchy condensation test for series with positive, decreasing terms.
Homework for Friday: Do problems 13, 15, 17, 19, 21, 23, and 29 on page 604 in section 10.3 and problem 6 on page 649 in Problems Plus (about summing the series whose terms are the reciprocals of the positive integers whose only prime factors are 2 and 3).
Friday, November 1
We discussed the ratio test and the alternating series test (material in section 10.4 of the textbook).
Homework for Monday: Read section 10.4. Do problems 5, 7, 9, 11, 19, 21, 29, 31, and 33 on pages 611-612 in section 10.4 and problem 4 in Problems Plus on page 648.
Monday, November 4
We discussed finding the radius of convergence of a power series by using the ratio test and the (not in the book) root test.
Homework for Wednesday: Read section 10.5. Do problems 3, 5, 7, 9, 19, 23, and 25 on page 617 in section 10.5 and problems 9 and 15 on pages 650-651 in Problems Plus.
Wednesday, November 6
We discussed differentiation and integration of power series.
Homework for Friday: Read section 10.6 and do problems 1, 5, 7, 11, 13, 19, 25, 29, and 31 on pages 622-623.
Friday, November 8
We discussed polynomial approximations to functions and error estimates for the approximations.
Homework for Monday: Read section 10.7. Know the boxed formulas on page 630. Do problems 3, 9, 19, 33, 39, 41, and 45 on page 633 in section 10.7.
Monday, November 11
We continued the discussion of how to obtain power series expansions of functions.
Homework for Wednesday: Read section 10.8. On page 570 in the Chapter 9 review problems, do the odd-numbered problems 1-11.
Wednesday, November 13
We discussed Pascal's triangle and the binomial expansion.
Homework for Friday: Do problems 3, 5, 9, 11, and 13 on pages 636-637 in section 10.8 and the odd-numbered problems 1-23 on page 646 in the Chapter 10 review.
Friday, November 15
We discussed applications of power series and remainder estimates in the context of the story "Lucky Numbers" from Richard Feynman's memoirs "Surely You're Joking, Mr. Feynman!"
Homework for Monday: Do problems 19, 23, 25, and 27 on pages 644-645 in section 10.9 and problems 15, 19, 21, 25, and 27 on pages 570-571 in the Chapter 9 Review.
Monday, November 18
We discussed some problems about surface area and looked at two sample problems for the second examination to take place on Friday, November 22.
The homework is to continue reviewing for the examination.
Wednesday, November 20
We discussed solutions to the sample problems for the second examination.
The homework is to prepare for the examination to be given Friday.
Friday, November 22
Second examination
Monday, November 25
We discussed the second examination and began talking about three-dimensional geometry.
Wednesday, November 27
No class meeting. Enjoy the Thanksgiving holiday!
Monday, December 2
We discussed three-dimensional coordinate systems.
Homework for Wednesday: Read sections 11.1 and 11.2 and do the Suggested Homework problems for section 11.1 that are posted at the main Math 152 web site.
Wednesday, December 4
We discussed product operations on three-dimensional vectors: the scalar (dot) product and the vector (cross) product.
By popular demand, the due date for the project is pushed back to Tuesday, December 10, the last day of classes for the semester. (Note, however, that the university has used the Humpty-Dumpty principle to redefine that day to be a Thursday.)
Homework for Friday: Read section 11.3 and do the Suggested Homework problems for section 11.2 that are posted at the main Math 152 web site.
Friday, December 6
We discussed the analytic description of planes in space.
Homework for Monday: Do problems 13, 15, 19, 23, 29, 31, and 37 in section 11.4 (page 681) and problems 1-11 (odd numbers) and 19-25 (odd numbers) in section 11.3 (page 673).
Monday, December 9
We filled out the course evaluation forms and continued the discussion of lines and planes in three-dimensional space.
Special office hours for final exam period: 1:00-3:00 on Friday, December 13 and Monday, December 16 in Milner 202.