# Math 130: Calculus I

```   Department of Mathematics and Computer Science
Hobart and William Smith Colleges

Fall, 2010.

Instructor:  David J. Eck.

Monday, Wednesday, Friday, 12:20 -- 1:55 PM, Room Napier 101.
Lab: Tuesday, 1:30 -- 2:55 PM, Gulick 206A.
```

Calculus I is a course in differential calculus, which is primarily the study of change and, in particular, of rates of change. Calculus is a fundamental tool in the sciences and social sciences, where the formulas that govern natural and social processes are often expressed in terms of rates of change. For example, Isaac Newton's famous laws of motion are expressed in terms of quantities such as velocity and acceleration. Velocity is simply the rate of change of position, while acceleration is the rate of change of velocity.

More generally, calculus is sometimes thought of as the study of the infinite and of the infinitesimal. Scientists, mathematicians, and philosophers have struggled for thousands of years to deal with the infinitely large and infinitely small. Calculus is the tool that has finally tamed these concepts, at least to some small extent. So in both theory and practice, Calculus is one of the crowning achievements in intellectual history. You should try to keep that in mind if you find yourself getting bogged down in formal rules and computational details -- those things, although essential, are not at the heart of the subject.

The textbook for this course is Single Variable Calculus: Early Transcendentals, by William Briggs and Lyle Cochran (ISBN 978-0-321-66414-3). Chapter 1 of this book is a review of some prerequisite material; we will spend about four class periods going quickly over some of the topics in this chapter. We will spend the rest of the course on Chapters 2, 3, and 4.

### Homework Assignments

I will assign homework problems from the textbook. Assignments will be posted on the course web page (http://math.hws.edu/eck/math130) as well as announced in class. I will collect only some of the homework for grading, but you should do all the other homework problems for practice. In fact, the more problems you do, the better you will understand the material and the more prepared you will be for later material. Calculus is a highly sequential, cumulative subject, and it is very important that you build a strong foundation of understanding and that you don't fall behind. If you find that additional practice is necessary, you can select additional problems from the textbook to work on.

The solutions that you turn in for grading should be written up clearly and should show all work. Explanations and justifications should be provided in clear English when appropriate, such as when the problem asks for an explanation or when it is not immediately clear why a certain step in a solution is valid. You will get no credit for simply stating an answer.

Answers to odd-numbered problems are in the back of the book, so I will generally collect only even-numbered problems. However, I might assign a few odd-numbered problems, since I can still grade the solution process, reasoning, and presentation.

You can work with other students on homework problems. You can get help from me, from the math intern, and from anyone else who will help you. However, you are required to write up your own set of solutions to turn in, and they should not be identical to other students' solutions. You should make sure that you really understand the work that you turn in.

I will collect homework once a week. Ordinarily, homework from a given week will be collected on Wednesday of the following week.

### Labs

This course has a required lab component, which meets every Tuesday from 1:30 to 2:55. During the lab, you will work in a group of three or four students on a set of problems that will be handed out during the lab. Some of the problems will be for practice. Others will be handed in as part of a lab report. Your group can turn in a single lab report, for which you will all receive the same grade. I suggest that you divide the work of writing up the lab report among all the members of the group. (If you really prefer not to share the grade with the rest of your group, you can write up and turn in a lab report on your own, to receive a separate grade from your group. However, you are still required to work with a group in lab.)

In general, the problems that I ask you to turn in as part of a lab report will not be simple calculations. They will often require some experimentation and deep thinking. They might not have a single, correct solution. The lab report should not simply state a solution. It should discuss the problem, how you approached it, and how you tried to solve it. You can receive substantial credit even if you don't solve the problem at all. Your discussion should be written up as an essay, in clear sentences and paragraphs. Treat each problem as a small writing assignment!

Except in extraordinary circumstances, you must be present at lab to get any credit.

Lab reports will ordinarily be collected on Monday of the week after the lab.

### Tests and Quizzes

There will be a short quiz at the beginning of class approximately once per week, usually on Friday. There will be no quiz in the first week of class or in weeks when there is a test. The first quiz will be on Friday, September 10. Quiz questions will often be taken directly from homework or from labs. Your lowest quiz grade will be dropped, and the remaining quiz grades will be averaged to give one overall grade for quizzes.

There will be three in-class tests, which will be given on the following Fridays: September 24, October 22, and November 19. The final exam for the course will take place at the time scheduled by the Registrar's office: Thursday, December 16, 8:30 -- 11:30 AM. The final exam will cover material from the entire term, with some emphasis on material that is covered after the third in-class test.

Basic scientific, non-graphing calculators will be provided for use on the tests and final exams. They will also be provided for quizzes in cases where they might be useful. You are not permitted to use your own calculator.

Note that except in extraordinary circumstances, there will be no make-up quizzes or exams. A missed quiz or exam will be graded as zero.

At the end of the semester, you will have grades for the following:

```            First Test
Second Test
Third Test
Homework
Labs
Quizzes
Final Exam
```

I reserve the right to adjust your grade downwards if you miss more than a couple of classes without a good excuse. In my grading scale, an A corresponds to 90--100%, B to 80--89%, C to 65--79%, D to 55--64%, and F to 0--54%. Grades near the endpoints of a range get a plus or minus.

### Office Hours, E-mail, and Web

My office is room 313 in Lansing Hall. My office phone extension is 3398. I am on campus most days, and you are welcome to come in any time you can find me there. My regular office hours, when I am almost certain to be in my office, are:

```        Monday, Wednesday, and Friday:   11:00 -- 12:00 and 1:30 -- 2:30

Tuesday:   12:00 -- 1:00
```

My e-mail address is eck@hws.edu. E-mail is good way to communicate with me, since I usually answer messages within a day of the time I receive them.

There is a short Web page for this course at http://math.hws.edu/eck/math130/f10/index.html. I will post weekly readings and assignments on that page.

### Math Intern

The Colleges employ a "math intern" who is available on a regular schedule to help students in calculus and precalculus courses. This year, the intern is Emma Daley (William Smith '10). Math intern hours are:

```           Sunday through Thursday
3:00 -- 5:30 and 6:30 -- 10:30 PM
Room Lansing 310
```

(The Tuesday evening time slot will be covered by a student teaching assistant, Yaoxin Liu.)

### From the CTL

The Center for Teaching and Learning has the following statement on disability accommodations: "If you are a student with a disability for which you may need accommodations, you should self-identify and register for services with the Coordinator of Disability Services at the Center for Teaching and Learning (CTL), and provide documentation of your disability. Disability related accommodations and services generally will not be provided until the registration and documentation process is complete. The guidelines for documenting disabilities can be found at the following website: http://www.hws.edu/disabilities.

### Tentative Schedule

Here is a tentative weekly schedule of topics for the course:

Dates Topic Sections
Aug. 30; Sept. 1, 3 Review of functions and graphs 1.1,1.2,1.3
Sept. 6, 8, 10 Trig review. Introduction to limits. 1.4,2.1,2.2
Sept. 13, 15, 17 Computing limits. The formal definition. 2.3,2.7(part)
Sept. 20, 22, 24 Limits and Infinity.
Test on Friday, September 24.
2.4,2.5
Sept. 27, 29; Oct. 1 Continuity. Introduction to derivatives. 2.6,3.1,3.2
Oct. 4, 6, 8 Derivative rules. 3.3,3.4
Oct. 13, 15 Rates of change. The chain rule.
Fall Break, Monday, October 11.
3.5,3.6
Oct. 18, 20, 22 Implicit differentiation.
Test on Friday, October 22
3.7
Oct. 25, 27, 29 More derivative rules. 3.8,3.9
Nov. 1, 3, 5 Related rates. Maxima and minima. 3.10,4.1
Nov. 8, 10, 12 Derivatives and graphing. 4.2,4.3
Nov. 15, 17, 19 Optimization problems.
Test on Friday, November 19.
4.4
Nov. 22 Linear approximation.
Thanksgiving break, November 24,26
4.5
Nov. 29; Dec. 1, 3 Mean Value Theorem. L'Hopital's Rule. 4.6,4.7
Dec. 6, 8, 10 Antiderivatives. 4.8
Dec. 16 Final Exam: Thursday, December 16, 8:30--11:30 AM