Record of daily activities, Math 152, Engineering Mathematics II, Honors Sections 201-202, Fall 2004

Monday, August 30
We looked at some motivating examples for studying calculus (the birdcage problem, understanding rainbows); we 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:
  1. Review sections 6.4 and 6.5 in the textbook (pages 389-406).
  2. Know the table of integrals on page 394.
  3. Do as many of the odd-numbered review problems (which 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 1
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 3
We discussed the method of finding volume by integrating the area of the cross section (the bread-slicing principle).
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 6
We discussed the computation of volumes by shells (the Russian-doll method), and we solved the napkin-ring problem.
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 8
We worked on some volume problems: the torus (both by washers and by shells), the birdcage, and the intersection of spheres.
Homework for Friday:
  1. Finish the problem your group was working.
  2. Read page 454.
  3. Do "Problems Plus" 1, 13, and 15 on pages 455-456.
Friday, September 10
We discussed some of the homework problems.
Homework for Monday: Do "Problems Plus" 3, 7, 25, and 31 on pages 455-457.
Monday, September 13
We discussed some of the homework problems, and we looked at an example of computing work via integration.
Homework for Wednesday: Read section 7.4 and work the Suggested Homework problems for section 7.4 that are posted at the main Math 152 web site.
Wednesday, September 15
We discussed the notion of the average value of a function, and we worked on problems 1, 5, 9, 12, 13, and 15 in section 7.5.
Homework for Friday: Read section 7.5 and finish those six problems.
Friday, September 17
We discussed the method of integration by parts and did examples.
Homework for Monday: Read section 8.1 and work the Suggested Homework problems for section 8.1 that are posted at the main Math 152 web site.
Monday, September 20
We discussed integrating products of trigonometric functions.
Homework for Wednesday: Read section 8.2 and work the Suggested Homework problems for section 8.2 that are posted at the main Math 152 web site.
Wednesday, September 22
We discussed integration via trigonometric substitution.
Homework for Friday: Read section 8.3 and work the Suggested Homework problems for section 8.3 that are posted at the main Math 152 web site.
Friday, September 24
We discussed integrating rational functions via the method of partial fractions.
Homework for Monday: Read section 8.4 and work the Suggested Homework problems for section 8.4 that are posted at the main Math 152 web site.
Monday, September 27
By way of review for the first examination, we looked at an old exam.
Homework for Wednesday: Prepare for the exam.
Wednesday, September 29
First examination
Friday, October 1
The graded examinations were returned, and we discussed improper integrals.
Homework for Monday: Read section 8.9 and work the Suggested Homework problems for section 8.9 that are posted at the main Math 152 web site.
Monday, October 4
We discussed error estimates for methods of numerical integration.
Homework for Wednesday: Read section 8.8 and work the Suggested Homework problems for section 8.8 that are posted at the main Math 152 web site.
Wednesday, October 6
We discussed the method of separation of variables for solving differential equations.
Homework for Friday: Read section 9.1 and work the Suggested Homework problems for section 9.1 that are posted at the main Math 152 web site.
Friday, October 8
We discussed separable differential equations, first-order linear differential equations, and Bernoulli differential equations.
Homework for Monday: Read section 9.2, work exercise 25 on page 541 in addition to the Suggested Homework problems for section 9.2 that are posted at the main Math 152 web site, and do numbers 2 and 10 on page 573 in Problems Plus.
Monday, October 11
We discussed the Problems Plus from the homework and the computation of arc length.
Homework for Wednesday: Read section 9.3, work the Suggested Homework problems for section 9.3 that are posted at the main Math 152 web site, and do number 6 in Problems Plus on page 573.
Wednesday, October 13
We discussed the computation of surface area of surfaces of revolution.
Homework for Friday: Read section 9.4, and work exercise 33 on page 554 in addition to the Suggested Homework problems for section 9.4 that are posted at the main Math 152 web site.
Friday, October 15
We discussed some of the homework problems and the computation of center of mass.
Homework for Monday: Read section 9.5 and do the Suggested Homework problems for section 9.5 that are posted at the main Math 152 web site.
Monday, October 18
We discussed hydrostatic pressure and hydrostatic force.
Homework for Wednesday: Read section 9.6 and do the Suggested Homework problems for section 9.6 that are posted at the main Math 152 web site.
Wednesday, October 20
We discussed sequences and limits of sequences.
Homework for Friday: Read section 10.1, do problem 15 in Problems Plus on page 574, and do the Suggested Homework problems for section 10.1 that are posted at the main Math 152 web site.
Friday, October 22
We discussed limits of sequences, the principle that a bounded increasing sequence converges, and the notion of convergence of infinite series.
Homework for Monday: Read Appendix E, pages A32-A33, and do in Exercises E on page A34 numbers 1 and 8.
Monday, October 25
We discussed convergence of infinite series in general and geometric series in particular.
Homework for Wednesday:
  1. Read section 10.2, pages 586-592.
  2. Do the Suggested Homework problems for section 10.2 that are posted at the main Math 152 web site.
  3. Suppose you eat 1/4 of a pizza, then 1/9 of what remains, then 1/16 of what remains, and so on. (At meal n you eat 1/(n+1)2 of what remains.) In the limit, how much of the pizza do you consume?
Wednesday, October 27
We discussed methods for analyzing infinite series by comparing them with integrals or with other series.
Homework for Friday:
  1. Read section 10.3, pages 595-603.
  2. Do the Suggested Homework problems for section 10.3 that are posted at the main Math 152 web site.
  3. Do the snowflake problem: number 5 in Problems Plus on page 649.
Friday, October 29
We discussed the root test, the ratio test, and the alternating series test. The slides from the lecture are available.
Homework for Monday: Read section 10.4 and do the Suggested Homework problems for section 10.4 that are posted at the main Math 152 web site.
Monday, November 1
By way of review for the examination, we looked at an old exam.
Homework for Wednesday: study for the exam.
Wednesday, November 3
Second examination
Friday, November 5
We discussed power series and the radius of convergence.
Homework for Monday: Read section 10.5 and do the Suggested Homework problems for section 10.5 that are posted at the main Math 152 web site.
Monday, November 8
We discussed three topics in infinite series: finding new series from old ones; solving differential equations with series; approximating integrals with series. The slides from the lecture are available.
Homework for Wednesday:
  1. Read section 10.6, pages 618-622.
  2. Do the Suggested Homework problems for section 10.6 that are posted at the main Math 152 web site.
  3. Do exercise 34 on page 623 in section 10.6.
Wednesday, November 10
We discussed Maclaurin series and Taylor series.
Homework for Friday:
  1. Read section 10.7, pages 623-632.
  2. Do the Suggested Homework problems for section 10.7 that are posted at the main Math 152 web site.
  3. Also do exercise 50 on page 634.
Friday, November 12
We discussed Taylor's theorem.
Homework for Monday:
  1. Read section 10.9 and do the Suggested Homework problems for section 10.9 that are posted at the main Math 152 web site.
  2. Suppose you were to plot the functions y=cos(x) and y=1-x2/2 on the same graph with the x and y axes scaled in inches (1 inch = 1 radian) using a line thickness of 1 point (where 1 inch = 72 points).
    plot of the two graphs
    Over what interval of the x-axis would the two curves be indistinguishable? Why?
Monday, November 15
We discussed the binomial theorem and an excerpt from Richard Feynman's memoirs.
Homework for Wednesday: Read section 10.8 and do exercises 3, 5, 11, and 13.
Wednesday, November 17
We discussed coordinates in three-dimensional space.
Homework for Friday:
  1. Read section 11.1, pages 652-656.
  2. Do the Suggested Homework problems for section 11.1 that are posted at the main Math 152 web site.
  3. Also do exercise 50 on page 657, which is a reminder about volume.
Friday, November 19
We discussed the scalar product (dot product) of three-dimensional vectors.
Homework for Monday:
  1. Read section 11.2, pages 657-664.
  2. Do the Suggested Homework problems for section 11.2 that are posted at the main Math 152 web site.
  3. Also do exercises 59 and 62 in section 11.2.
Monday, November 22
We discussed the vector cross product and the scalar triple product.
Class will not meet on Wednesday, November 24.
Have a safe Thanksgiving holiday!
Monday, November 29
We discussed the dot product, the cross product, and how they appear in the theory of Hamilton's quaternions.
Homework for Wednesday:
  1. Read section 11.3.
  2. Do the Suggested Homework problems for section 11.3 that are posted at the main Math 152 web site.
  3. Also do exercise 26 on page 673 in section 11.3.
Wednesday, December 1
We discussed equations of lines and planes in space.
Homework for Friday: Read section 11.4 and do the Suggested Homework problems for section 11.4 that are posted at the main Math 152 web site.
Friday, December 3
We looked at some past common exams by way of review.
Monday, December 6
We looked at a past final examination.
Reminder: the final examination is scheduled for Tuesday, December 14, 3:30-5:30 pm.
Tuesday, December 14
Final examination