f Math 131: Calculus II

# Math 131: Calculus I

```   Spring, 2005.

Instructor:  David J. Eck.

Monday, Wednesday, Friday, 11:15--12:10,
Napier 101.

Lab:  Tuesday, 10:20--11:45 AM,
Gulick 206A.
```

Math 131 is the second term of calculus. For the most part, it deals with what is known as "the integral calculus." As far as calculus is concerned, integration is an inverse operation to differentiation, which you studied in Calculus I. In order to succeed in Calculus II, you will have to build on an understanding of the differential calculus. It is particularly important that you know the many formulas for taking derivatives. Familiarity with the idea of "limit" will also be very important. Applications such as max/min problems, curve sketching, and related rates are less important, although they will occasionally show up in problems.

The textbook for the course is Calculus of a Single Variable / Early Transcendental Functions, third edition, by Larson, Hostetler, and Edwards. This is the same textbook that was used in Calculus I in the fall term. We will cover material from Chapter 4 through the middle of Chapter 8. A copy of the solutions manual for odd-numbered problems in the textbook will be on reserve in the library.

The course can be divided into four parts:

• Part I: Integration (Sections 4.1 -- 4.8). This part of the course introduces two types of integrals, known as the indefinite integral (or antiderivative) and the definite integral, and it covers basic integration formulas.
• Part II: Applications of Integration (Sections 5.1, 5.2, and 6.1 -- 6.6). This part covers some of the ways in which integrals can be used in the real world in applications such as computing volume, predicting population growth, and finding quantity of work done.
• Part III: Techniques of Integration (Sections 7.1 -- 7.8). There is no complete set of formulas for computing integrals (as there is for derivatives). But there is a toolbox of techniques that can be applied. This part of the course covers some of these tools.
• Part IV: Infinite Series (Selections from Chapter 8). For the last two weeks of the course, we move from integration to another application of limits: taking the sum of an infinite number of terms.

### Labs

This course has a required lab component. Each lab will begin with a few warm-up exercises, and then move on to more challenging problems. I will collect one or two of these problems for grading, either at the end of lab or in class the next day. In general, you will want to work on these problems in a group and turn in a group solution.

Please bring your textbook to lab. Some of the lab problems will be from the book.

### Homework

Each week, I will assign a fairly small number of exercises from the textbook to be handed in as homework. You are allowed to work with other people on the homework, but you should write up the solutions on your own, in your own words. The goal is not just to solve the problem, but to present the solution in an organized, clear, mathematically correct way. Your solutions will be graded for presentation and style, as well as for correctness. In no case will you get any points simply for stating a correct final answer.

In addition to the homework that I collect, I will suggest additional problems for you to work on. You should do all these problems and as many more as are necessary for you to master the material.

### Math Department Speakers

From time to time, the Mathematics Department sponsors talks by various speakers from outside the Colleges. As part of the requirements for this course, you should attend at least one of the talks. Attendance will count for ten percent of your homework grade -- a small part of your total grade for the course, but one that could easily make a difference on your final letter grade.

### Quizzes

There will be occasional 10-minute quizzes in class. In general, they will not be announced in advance (but you can expect the first one on Monday, January 24). The quizzes are meant to check on your understanding of basic facts. The questions will include such things as definitions, true/false questions, and relatively straightforward exercises. Some of the exercises will be taken from the labs or homework.

There will be about ten quizzes over the course of the term. There are no make-up quizzes, but the lowest quiz grade will be dropped.

### Tests

There will be three in-class tests, plus a final exam. The tests will be on Friday, April 11; Wednesday, March 9; and Friday, April 15. The final exam will take place during the regularly scheduled exam period, on Sunday, May 8, in our regular classroom.

The first test will cover Chapter 4, the second will cover Chapters 5 and 6, and the third will cover Chapter 7. The final exam will be cumulative, but will concentrate on Chapter 8.

Your grade for the course is based on labs, homework, quizzes, three in-class tests, and a final exam. These count for the following fractions of the grade:

```         Labs            1/8
Homework        1/8
Quizzes         1/8
Test 1          1/8
Test 2          1/8
Test 3          1/8
Final exam      2/8
```

### Attendance and other Policies

I do not take attendance, but I assume that you understand the importance of being in class. Note that I will give unannounced quizzes, and that there are no make-ups for these quizzes. I will also collect work in the labs that cannot be made up, but again, I will drop your lowest lab grade. You should make every effort to be present for tests. If you are forced to miss a test because of circumstances that I agree are truly beyond your control, I will give you a make-up test.

I expect you to maintain a reasonable level of decorum in class. This means that there is no eating or drinking in class. Cell phones are turned off. There is no walking in late or walking in and out of the room during class.

### Math Intern

Robert Klein, a recent graduate of Hobart and William Smith Colleges with a major in mathematics, will be the Mathematics Department's "math intern" for the Spring term. He will be holding regular office hours on the third floor of Lansing Hall. You are encouraged to use his office hours as a resource for any extra help that you need in the course. (The math intern is a supplement to, not a replacement for, the help that you can get from your professor!)

### Office Hours, Email, WWW

My office is room 301 in Lansing Hall. My office phone extension is 3398. I am on campus most days, and you are welcome to come in anytime you can find me there. I will announce regular office hours (times when I promise to try my best to definitely be in my office) as soon as I schedule them.

My email address is eck@hws.edu. Email is good way to communicate with me, since I usually answer messages the day I receive them.

There is a Web page for this course, which can be found at http://math.hws.edu/eck/math131/index_s05.html. This page will list weekly homework assignments, and it will have a link to each week's lab.

### Tentative Schedule

The following schedule of readings from the text is tentative. It includes most of the sections from Chapters 4 through 7 of the textbook, plus about half of Chapter 8. Depending on how things go, we might need to omit some of this material. However, we will definitely cover the major topics.

When What
January 17, 19, 21 Sections 4.1, 4.2, 4.3
January 24, 26, 29 Sections 4.4, 4.5
January 31; February 2, 4 Sections 4.6, 4.7
February 7, 9, 11 Sections 4.8, 5.1
Test on Friday, February 11
February 14, 16, 18 Sections 5.2, 6.1
February 21, 23, 25 Sections 6.2, 6.3
February 28; March 2, 4 Sections 6.4, 6.5
March 7, 9 Section 6.6
Test on Wednesday, March 9
Spring Break, March 11 to 20
March 21, 23, 25 Sections 7.1, 7.2, 7.3
March 28, 30; April 1 Sections 7.4, 7.5
April 4, 6, 8 Sections 7.6, 7.7
April 11, 13, 15 Sections 7.8, 8.1
Test on Friday, April 15
April 18, 20, 22 Sections 8.2, 8.3
April 25, 27, 29 Sections 8.4, 8.7
May 2 More material from Chapter 8
Last day of class
Sunday, May 8 Final Exam
7:00 PM, in our regular classroom