The course described on this page ended May 8, 2005

MATH 131: Calculus II


   Department of Mathematics and Computer Science
   Hobart and William Smith Colleges

   Spring, 2005.

   Instructor:  David J. Eck  (eck@hws.edu)

   Monday, Wednesday, Friday, 11:15--12:10 AM.
   Room Napier 101.
   
   Lab:  Tuesday, 10:20--11:45 AM,
   Gulick 206A.

   Course Handout:  http://math.hws.edu/eck/courses/math131_s05.html

Lab Worksheets
Lab 1: January 18 Lab 2: January 25 Lab 3: February 1
Lab 4: February 8 Lab 5: February 15 Lab 6: February 22
Lab 7: March 1 Lab 8: March 8 Lab 9: March 22
Lab 10: March 29 Lab 11: April 5 Lab 12: April 12
Lab 13: April 19 Lab 14: April 26 Lab 15: May 3

End of Term

Our final class meeting is on Monday, May 2. There is one more lab, on May 3, which will be a review for the final exam. The final exam will be given at 7:00 PM on Sunday, May 8. It will be in our usual classroom.

Here are my office hours for the final week of the term:

          Monday, May 2:      12:00 -- 1:30 PM
          Wednesday,  May 4:   2:00 -- 4:00 PM
          Thursday, May 5:    12:00 -- 2:00 PM
          Saturday, May 7:    11:00 AM -- 2:00 PM
          Sunday, May 8:       2:00 -- 4:00 PM

Fourteenth Week: April 25, 27, and 29

We will finish up the course by looking at power series and Taylor series. I will cover a bit of the material from Sections 8.7 and 8.9 in class, but I do not necessarily expect you to read these sections yourself. You should read Section 8.8 and pages 632 to 636 in Section 8.10.

I will not collect any homework on this material, but here are some suggested exercises for you to try:

            Section 8.8,  # 5, 7, 19, 21
            Section 8.9,  # 19, 21, 23
            Section 8.10, # 1, 3, 5

Thirteenth Week: April 18, 20, and 22

We will be covering topics from Chapter 8 this week. The reading consists of Sections 8.1 and 8.2 plus some material from Sections 8.3 and 8.4. From Sections 8.3, you only need to know the basic facts about convergence and divergence of p-series (Theorem 8.11). From Section 8.4, you should know the Direct Comparison Test (pages 583-584). The following homework for the week is due in lab next Tuesday, April 26:

            Section 8.1, # 14, 48, 60, 62
            Section 8.2, # 14, 40, 44, 46
            Section 8.4, # 8, 12

Twelfth Week: April 11, 13, and 15

There is a test on Friday of this week. We will begin Chapter 8 in class this week, but it will not be on the test. Because of the test, there will be no homework due next week, and this week's lab will be a review for the test.

Eleventh Week: April 4, 6, and 8

We will cover L'Hopital's Rule and Improper Integrals (Sections 7.7 and 7.8) this week. Remember that there is a test coming up on Friday of next week. It will cover Chapter 7. The following homework is due in lab next week:

         Section 7.7, # 12, 18, 20, 24, 42b
         Section 7.8, # 10, 14, 30, 32, 44

Tenth Week: March 28 and 30; April 1

By the end of the week we should be mostly finished with the section of the course on "techniques of integration." The reading for the week is Sections 7.3, 7.4, and 7.5. I will be doing some examples from Section 7.4, but I will not assign any problems from this section or test you on it. We will not cover Section 7.6. The following homework is due in lab next Tuesday, April 5:

          Section 7.3: # 4, 10, 16, 30, 88
          Section 7.5: # 6, 12, 16, 20, 48

Ninth Week: March 21, 23, and 25

This week, we move on to Chapter 7, which is mostly about techniques of integration. We will cover Sections 7.1 and 7.2 this week, and possibly begin Section 7.3 on Friday. The following homework is due in lab next Tuesday, March 29:

          Section 7.1, # 24, 30, 48, 88
          Section 7.2, # 12, 18, 24, 28, 36, 84

Eighth Week: March 7 and 9

There is a test on Wednesday, March 9. An information sheet about the test is available. On Monday, we will be reviewing for the test. There is no new homework assignment for this week.

March 9 is the last day of class before Spring break. Class will resume on Monday, March 21.

Seventh Week: February 28; March 2 and 4

We will cover Sections 6.4 and 6.5 this week. This is probably the last material that we will cover from Chapter 6, although we might look briefly at some stuff from Section 6.6. The following homework from these sections will be due next week, on Tuesday, March 8:

          Section 6.4, # 4, 8, 32, 44
          Section 6.5, # 2, 10, 16

Remember that there is a test next Wednesday, March 9. It will cover Chapters 5 and 6.

Sixth Week: February 21, 23, and 25

The reading for the week is Sections 6.1, 6.2, and 6.3, which cover using integration to find areas and volumes. The following homework from these sections is due next Tuesday, March 1:

        Section 6.1: # 6, 20, 26
        Section 6.2: # 2, 6, 22, 48
        Section 6.3: # 4, 18, 36

Note, however, that you really need to do a lot of problems to understand this material. You should do as many of the odd-numbered problems from Sections 6.1, 6.2, and 6.3 as necessary to learn the techniques.

Fifth Week: February 14, 16, and 18

The main topic for the week will be differential equations and their application to exponential growth and decay problems. This material is from Chapter 5, but we will cover only part of this chapter. The reading from Chapter 5 is Section 5.1 and Section 5.2, pages 382 to 386 only. We will move on to Section 6.1 on Friday.

The following homework is due in lab next Tuesday:

          Section 5.1, # 6, 26, 40, 42, 50, 74
          Section 5.2, # 28, 46, 50, 65

Here are the two Calculus II applets that I demonstrated in class on Friday, February 18.

Fourth Week: February 7, 9, and 11

There will be a test this week on Friday, February 11. It will cover sections 4.1 through 4.8. More information about the test can be found on the worksheet for this week's lab. I will have extra office hours before the exam. I expect to be available in my office on Thursday between 10:00 and 2:00 and on Friday between 10:00 and 11:00.

We started Section 4.6 on Friday of last week. We will finish it on Monday. We will also covert Section 4.8, which is very short, on Monday. On Wednesday, we will review for the test. We might also do some material from Section 4.9. However, any new material that we cover on Wednesday will not be on the test.

Here are some suggested exercises from Sections 4.6 and 4.8. These problems will not be collected or graded:

           Section 4.6, # 3, 25, 35, 49
           Section 4.8, # 1, 7, 15, 27

Third Week: January 31; February 2 and 4

We will cover Sections 4.5 and 4.7 this week. By the end of the week, we should start Section 4.6. The following homework is due next week at lab, on Tuesday, Bebruary 8:

           Section 4.5: # 30, 34, 50, 58, 66, 86
           Section 4.7, # 6, 30, 32, 46

Second Week: January 24, 26, and 28

The reading for the week is Sections 4.3 and 4.4. It is possible that we will start Section 4.5 by Friday. (We did not get to do Section 4.3 last week.) The following is the homework for the week. It can be turned in at lab next week, on Tuesday, February 1.

           Section 4.3, # 12, 28, 30, 42
           Section 4.4, # 10, 22, 38, 48, 90, 102

First Week: January 17, 19, and 21

The reading for the first week of the course is Sections 4.1, 4.2, and 4.3. Section 4.1 introduces the antiderivative and the indefinite integral. You should already have encountered these topics at the end of Calculus I, but we will review them on the first day of class and in the first lab. The main topic, however, will be the definite integral and its relation to the area under a curve.

The following homework is due in class next Monday, January 24:

            Section 4.1:  # 26, 40, 62, 68, 88
            Section 4.2:  #  8, 26, 30, 42, 52