This course endedon May 9, 2020

## Math 130: Calculus I

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

Spring 2020.

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

Syllabus:  http://math.hws.edu/eck/courses/math130_s20.html

Textbook:  Calculus, Volume 1, from openstax.org

```

### Ninth Week and Beyond...

Because of the COVID-19 pandemic, we are moving to entirely on-line teaching. The main hub for the course will be on Canvas. Students should check there for further updates and assignments.

See the syllabus revisions: Part 1 and Part 2.

### Eighth Week: March 9, 11, and 13

There is a test in class on Wednesday, March 11. A study guide for the test was handed out in class on Friday.

We will spend at least part of the class on Monday going over material for the test, and the lab on Tuesday will also be review for the test.

Aside from the test, we should cover Section 3.8, on implicit differentiation. That will finish Chapter 3 and get us ready for Chapter 4, which covers applications of the derivative. The rest of the semester will be spent in Chapter 4.

### Seventh Week: March 2, 4, and 6

We started looking at inverse functions and their derivatives on Friday. We will continue that on Monday. The reading on derivatives of inverse functions is Section 3.7, but you might also look at Section 1.4, which reviews inverse functions. We will then skip Section 3.8 temporarily and move on to Section 3.9 exponential and logarithmic functions and their derivatives. We will spend some time reviewing exponentials and logarithms; you can find that material in Section 1.5.

The second test is coming up next week, on Wednesday, March 11. It will cover Chapter 3 except for Section 1.8.

### Sixth Week: February 24, 26, and 28

This week, we will cover Section 3.5 (derivatives of trigonometric functions) and Section 3.6 (the chain rule). The next topic coming up is derivatives of inverse functions, in Section 3.6. We might start that by Friday, but before covering Section 3.6, we will review the idea of inverse function, including the inverse trigonometric functions.

### Fifth Week: February 17, 19, and 21

We started Section 3.3 last Friday, and we will continue it on Monday. This section covers basic rules for differentiation such as the sum, product, power, and quotient rules. We will move on to Section 3.4, which covers rates of change. After that, we will take some time to review trigonometric functions, in preparation for looking at their derivatives.

Here is a link to the "derivatives" program that we looked at in class last Friday:

http://math.hws.edu/eck/js/graphs/derivatives.html

Earlier, we looked at a web page that can do lots of different math operations:

https://www.wolframalpha.com/

### Fourth Week: February 10. 12, and 14

There is a test on Wednesday of this week. A study guide was handed out in class on Friday. We managed to cover Section 3.1 on Friday, so the test will cover Chapter 2 and Section 3.1. Section 3.1 covered the definition of the derivative at a point, and how it represents the slope of a tangent line or the instantaneous velocity.

After the test, we will move on to Section 3.2 and possibly begin Section 3.3.

### Third Week: February 3, 5, and 7

We will finish Section 2.4 by covering the Intermediate Value Theorem and its applications. We will then look at the formal definition of derivative in Section 2.5. You are required to understand this definition geometrically and to be be able to use it in simple proofs; however, we will not do anything very complicated with it. We should have time to start Chapter 3 this week.

The first test of the semester is coming up next week, on Wednesday, February 12. It will cover Chapter 2 and the definition of the derivative.

### Second Week: January 27, 29, and 31

The reading for the week is Section 2.3 and starting Section 2.4. At the beginning of the week, we have one short topic, infinite limits, to finish up from Section 2.2. We will spend the rest of Monday and Wednesday on Section 2.3. We will see that most limits as x approaches a of a function f(x) can be evaluated by "plugging a into f(x)". However, the interesting cases happen when this simple approach does not apply. We will look at various techniques for evaluating limits that cannot be evaluated simply by plugging in.

By Friday, we will start Section 2.4, which covers continuity. As I have already mentioned, continuity and limits are very closely connected. Continuity is conceptually the simpler concept, and it is possible to understand limits in terms of continuity. But the approach that is actually taken is to define continuity in terms of limits. We will look at the definition of continuity and see what it means for graphs of functions. There are some important consequences of continuity that we will probably not get to this week, so we will finish Section 2.4 next week.

### First Week: January 22 and 24

Welcome to the course!

The reading for the week is Section 2.1 and Section 2.2. These sections introduce Calculus and the concept of limits, which are an essential tool for understanding and doing calculus. You should do this reading before class on Friday. It is not impossible that there will be a quiz on Friday that could include questions about the reading.

You should also carefully read the syllabus for the course.

The first lab of the course is on Tuesday, January 21. Although that is before the first lecture, we will have a lab on that day, and work from that lab will be due in class on Friday, January 24.