## Math 131: Calculus II

   Department of Mathematics and Computer Science
Hobart and William Smith Colleges

Spring 2011.

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

Course Handout:  http://math.hws.edu/eck/courses/math131_s11.html

Monday, Wednesday, Friday, 9:05--10:00 AM, Room Eaton 111.
Lab:  Thursday, 8:45--10:10 AM, Room Gulick 206A



### End of Semester: May 2 and 9

The final class is on Monday, May 2. The final exam is next Monday, May 9, at 8:30 AM. It will be held in our regular classroom.

Here is the final exam information sheet. You can also consult the review sheets for the first test, for the second test, and for the third test.

### Week 14: April 25, 27, and 29

We will be working on Chapter 9. Most of the material that we will look at is in Section 9.2. We will also cover parts of the other sections in that chapter. The main topics is \textit{Power Series}, including their intervals of convergence. We will use (but not prove) that a power series can be integrated or differentiated term-by-term. We will also look at Taylor series and Taylor polynomials.

The final exam is on Monday, May 9 at 8:30 AM. An information sheet is available.

### Week 13: April 18, 20, and 22

We continue with Chapter 8, Infinite Series, for the entire week. From Section 8.5, we will cover only the Comparison Test and the Root Test. From Section 8.6, we cover absolute convergence, conditional convergence, and the Alternating Series Test. We will also encounter a few "power series," which are not covered officially until Chapter 9.

### Week 12: April 11, 13, 15

For the remainder of the semester, we will be working on infinite series. This material will make up about half of the final exam, with the remaining part of the exam covering previous sections of the course.

We start with Section 8.3 and 8.4 this week. We will look at the definition of infinite series and of the sum of an infinite series. We will look at two special types of series: geometric series [very important] and telescoping series [rare and not very important]. And we will be looking at the first of several convergence tests for infinite series, the integral test and the n-th term test for divergence.

### Week 11: April 4, 6, and 8

There is a test next week, on Monday, April 11. An information sheet is available.

After finishing up one more example of improper integrals, we will move on to Chapter 8. We will cover Sections 8.1 and 8.2 on Monday and Wednesday. Material on infinite from those sections can be on the test next Monday. (There won't be anything on the test on infinite series.) On Friday, we will start Section 8.3 if there is time after reviewing for the test.

I haven't assigned any homework for this week, since there won't be time for you to do it and get it graded before the test. However, here are some recommended straightforward problems in Sections 8.1 and 8.2:

            Section 8.1, # 9, 15, 25, 27
Section 8.2, # 9, 11, 13, 27, 31


### Week 10: March 29 and 31; April 1

We will start the week with Partial Fractions, Section 7.4, but we will only cover the case of linear factors, not irreducible quadratic factors. We will then do a few topics from the remainder of Chapter 7. We will not be doing anything in Section 7.5, and we have already done as much of Section 7.8 as we will ever do. (Some material from 7.8 -- differential equations, separation of variables, and initial value problems -- was covered in lab.) From Section 7.6, we will talk briefly about numerical integration, but you will not have to memorize the formulas for the Trapezoid rule or Simpson's rule. We will spend some time on Section 7.7, Improper Integrals, but it turns out that part of that topic as well has been covered in lab. s

### Week 9: March 21, 23, and 25

Coming off Spring Break, we start the third major section of the course, which covers techniques of integration, Chapter 7. This week, we cover Section 7.1, on Integration by Parts, and we will look at selected parts of Sections 7.2 through 7.4.

### Week 8: March 7, 9, and 11

There is a test on Wednesday of this week. An information sheet is available.

We will be doing mostly review on Monday. On Friday, rather than go on to Chapter 7, we will cover exponential growth and decay problems, from Section 6.8.

Next week is Spring Break. Have a great time!

### Week 7: February 28; March 2 and 4

We will cover Section 6.5 and parts of Section 6.6 this week. Section 6.5 is about arc length. I will add to that the formula for the area of a surface of revolution, but there will not be any homework or testing on surface area. For Section 6.6, we will talk a little about force and work in general, and we will cover "lifting problems." Section 6.5 starts with one-dimensional density problems, which we have already covered in a lab. (Later, we will do some problems with non-constant work, but that will not be on the test next week.) I will not cover the last part of 6.6, on pressure. We will skip over Sections 6.7 and 6.8 for the time being, though we might do parts of them later.

### Week 6: February 21, 23, and 25

The topic for Monday and Wednesday is finding volumes of rotation. We will finish Section 6.3, which covers the "disk method" and the "washer method" for finding volumes, and we will do all of Section 6.4, which covers the "shell method." On Friday, we will finish up a few volume examples and move on to Section 6.5 and arc length.

### Week 5: February 14, 16, and 18

We continue with the "applications of integration" part of the course. This week, after finishing Section 6.1, we will cover Section 6.2 and begin Section 6.3. Section 6.2 is about finding the area of a region bounded by two or more curves. This is partly a warm-up for Section 6.3, which introduces the idea of using integration to find volumes of solids of various sorts.

### Week 4: February 7, 9, and 11

There is a test on Friday. A information sheet is available.

We will finish up Chapter 5 on Monday. We will begin Chapter 6 on Friday, but any material that we cover from Chapter 6 is not on the test. Chapter 6 covers applications of integration. The reading is Section 6.1.

### Week 3: January 31; February 2 and 4

The reading for the week is Chapter 5, Sections 4 and 5. We will probably not quite finish Chapter 5 by the end of the week. Section 5.4 introduces the average value of a function on an interval, and it proves the Mean Value Theorem for integrals. Section 5.5 covers substitution, a useful technique for computing integrals (and the only one that we will have until we get to chapter 7).

We have a test coming up next week, on Friday, February 11. It will cover Chapter 5.

### Week 2: January 24, 26, and 28

The reading for the week is Sections 5.2 and 5.3. The highlight is the Fundamental Theorem of Calculus, and the main point is the fact that definite integrals can be calculated using antiderivatives. Before we get to that, though, we will have to get a little more definite about definite integrals and Riemann sums.

### Week 1: January 19 and 21

Classes start on Wednesday, January 19, and our first lab is Thursday, January 20. We will do just a bit of review of Calculus I on the first day of class and in the lab, and then we will start right in on Calculus II. The reading for the week is Section 5.1, which covers area under a curve, summation notation, and Riemann sums.