This courses ended December 16, 2010

## Math 130: Calculus I

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

Fall, 2010.

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

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

Course Handout:  http://math.hws.edu/eck/courses/math130_f10.html

```

## Study Table

Selena Sha, our lab TA, will hold a study table once a week for the rest of the semester, under the auspices of the Center for Teaching and Learning. The tables will be Tuesday evenings from 8:30 to 10:00.

You must sign up for the table in advance, no later than three hours before the meeting, using CTL's TutorTrac web site. Here are some

Instructions for making appointments using TutorTrac

and here is

A direct link to the TutorTrac web site

### Fifteenth Week and End Of Term: December 6, 8, 10

The final exam for this course is scheduled for Thursday, December 16, from 8:30 to 11:30 AM in our usual classroom. An information sheet about the final exam is available. You can also review the information sheets from the first test, the second test, and the third test.

The reading for the last week of the semester is Section 4.8. This section introduces antiderivatives and definite integrals and covers some of their very basic properties. Integrals are the major focus of Calculus II. Section 4.8 also introduces simple differential equations and initial value problems that can be solved using antiderivatives.

### Fourteenth Week: November 29; December 1 and 3

The reading for the week is Sections 4.6 and 4.7, which cover the Mean Value Theorem and L'Hopital's Rule. We will go throught the proof of the Mean Value Theorem and some of its consequences. We have already taken some of these consequences and being "obvious," and you should try to appreciate why mathematicians feel the need to prove things that seem obvious. L'Hopital's Rule is a technique that can be applied to evaluate many limits that would be very difficult without it.

### Twelfth and Thiteenth Weeks: November 15, 17, 19, and 22

With the test on Friday, November 19, we will not be getting much new material done in the week of November 15. However, we will be working on Section 4.4 (max/min word problems). We will continue with max/min problems on Monday, November 22. Note that we will skip Section 4.5.

There is no class on November 24 or 26 because of Thanksgiving break.

Have a greate Thanksgiving!

### Eleventh Week: November 8, 10, 12

By the end of the week, we will be done with Chapter 4, Sections 1, 2, and 3. These sections cover the first and second derivatives and their meanings. Concepts include increasing and decreasing functions, concavity, local and absolute maxima and minima, and inflection points.

There is a quiz on Friday on Sections 4.1 and 4.2. There is a test coming up Friday of next week. An information sheet for the test is available.

### Tenth Week: November 1, 3, 5

We will work on related rates, Section 3.10, for two classes this week. On Friday, we begin Chapter 4 by looking at critcal points, maximum ponts, minimum points, and inflection points of functions (Section 4.1).

The quiz on Friday will be on Sections 3.9 and 3.10.

### Ninth Week: October 25, 27, 29

We will do sections 3.8 and 3.9 this week, which cover differentiation rules for logarithmic, exponential, and inverse trigonometric functions. This includes functions such as xx, where neither the base nor the exponent are constant. We will spend a little time reviewing the functions sin-1(x) and tan-1(x).

There will be a quiz on Friday, on Sections 3.7 and 3.8.

### Eighth Week: October 18, 20, 22

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

We will finish Section 3.5 on Monday, which will finish all the material that will be in the test. On Wednesday, we will move on to Section 3.7, which covers implicit functions and implicit differentiation.

### Seventh Week: October 13 and 15

We will do Section 3.6 and begin Section 3.5 this week. Section 3.6 covers the chain rule, the last major general rule for computing derivatives. Section 3.5 is about the meaning of the derivative. It discusses the general idea of rate of change, and it introduces some applications of the derivative.

There is a quiz this Friday, which will be given at the end of class. It will concentrate on derivative rules from Sections 3.2 through 3.4. (It will not include the chain rule.)

There is a test coming up on Friday of next week, which will cover through Section 3.6.

### Sixth Week: October 4, 6, and 8

The reading for the week is Sections 3.2, 3.3, and 3.4. This includes the basic derivative rules (sum rule, product rule, quotient rule) as well as the derivatives of ex and of the trigonometric functions.

We never did get to Section 3.2 last week, so the homework that was due on October 6 is postponed to October 8. There will be a new homework assignment on Friday, which will be due the following week.

There is no quiz on Friday this week.

### Fifth Week: September 27 and 29; October 1

We will cover continuity and the Intermediate Value Theorem, Section 2.6, on Monday. This will finish Chapter 2. On Wednesday, we move on to Chapter 3, which introduces derivatives and techniques for computing them. We will cover Sections 3.1 and 3.2 this week.

Link to applets from Friday's class

### Fourth Week: September 20, 22, and 24

There is a test on Friday, September 24. An Information Sheet about the test is available.

We will finish Chapter 2, Section 5 on Monday. Note that this section will be covered on the test and is part of the homework that is due on Wednesday. In class on Wednesday, I will answer questions about the test. If any time remains, we will move on to Chapter 2, Section 6, but any new material that we cover on Wednesday will not be on the test.

Because of the test, there is no new homework assignment for this week. However, there is still a regular lab, and the lab report will be due, as usual, next Tuesday.

### Third Week: September 13, 15, and 17

After a few examples from Section 2.3, we will spend some time on the formal "epsilon-delta" (ε-δ) definition of limits. This is covered in the textbook in Section 2.7. You should read that section through the top of page 113. After that, we will look at infinite limits (Section 2.4) and we might start limits at infinity (Section 2.5) on Friday. We will finish Section 2.5 next Monday.

There is a quiz this week, and there is a test coming up next week, on Friday, September 24. The test will cover through Section 2.5, plus what we have done from Section 2.7.

### Second Week: September 6, 8, and 10

This week, we begin Calculus. After finishing up a couple comments on Chapter 1 (about inverses), we will move on to Chapter 2, which covers limits and continuity. The reading for the week is Sections 2.1, 2.2, and 2.3. The first two sections give an informal, intuitive introduction to limits and to the idea of instantaneous velocity. Section 2.3 covers some basic rules and techniques for calculating limits.

### First Week: August 30; September 1 and 3

The textbook for the course is Single Variable Calculus: Early Transcendentals by William Briggs and Lyle Cochran. Homework assignments will be made up of exercises from this book. You should try to get a copy of the book by September 1.

The first chapter of the textbook is review of prerequisite material. We will not cover all the details, be we will spend the first three or four class periods going over some of the major topics from that chapter. On Monday and Wednesday, we will go over functions and graphs. On Friday, we will work on exponential and logarithmic functions and possibly trigonometric functions.

Link to applets from Friday's class