Mary Parker

Math 1854, Calculus I

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Course handout / Homework / Graphing technology / Handouts, sample tests, etc.

What is calculus?

In calculus, we begin to deal, in a systematic way, with the continuous aspect of the functions we use to model phenomena in the real world. We learn how to generalize the idea about slope of a straight line to the "slope" of a curve, which is, of course, changing as the x value changes. We make various observations about this "slope" to solve all sorts of practical problems. And then this all leads into finding areas under curves. You've all found areas of objects whose sides are straight lines. And even circles. But lots of interesting shapes are more complicated than that. How do we find those areas? We'll learn those ideas in calculus and they are intrinsically related to this "slope" idea.

How do we do all of this? I can't give away the punch line here! You'll have to take the course to find out!

Style of the course and the text:

This course is a lot of fun to teach. The text we are using has some very interesting examples. As soon as you decide that you're going to enroll, go ahead and buy the book. Look at the very first problem in section 1. It's pretty interesting. (Actually, I find problem 7 in the same section even more interesting, but you'll understand 7 better if you read 1 first!)

Our text is one of the leaders in the new calculus movement, where we attempt to teach every topic in four ways - graphically, numerically, analytically (algebra), and verbally. In my experience, this helps even more students succeed in calculus than ever before and also helps them understand better how to use calculus in their other courses, like physics or engineering. If you look through the exercises in section 1 of chapter 1, you'll see some of the variety. Don't be upset if it doesn't look like the other math courses you have had. We don't expect you to be comfortable with all these different approaches at first. Chapter 1 doesn't even get to calculus ideas yet - it's just precalculus material with a focus on the variety of ways to look at it. One of our objectives in the calculus course is to increase your sophistication in "problem solving", which is enhanced by your knowing a variety of ways to approach problems. I try to give a mixture of easy and medium difficulty problems, with a few more challenging ones, and lots of help whenever you need it.

Prerequisite:

It is important that you know the prerequisite material before you start the course. That means that you need to know all the material typically covered in trig and precalculus courses. At ACC, College Algebra (MTH 1743) is not an acceptable substitute for Precalculus (MTH 1764 or MTH 1763) in preparing for this scientific calculus course. There are a number of important topics not covered (or covered much too briefly) in College Algebra that are covered in Precalculus. I have a study sheet on the Web to help you review precalculus topics. It includes some trigonometry, but, because so many students need to review trig specifically, I also have a trig review sheet, with answers and commentary. (The departmental review sheet for calculus, which we wrote a number of years ago, has answers for all of the problems. You're welcome to use it instead.)

Calculators:

At ACC we assume that you will have access to some form of graphing technology when you take our calculus courses. There are a variety of ways that you can do this. In previous semesters, most ACC calculus students have found that they really need something available at home, since they just don't have time to come in to the LRS or Computer Lab very often. But there are always a few students who make it work using the LRS and labs. In class, I'll be demonstrating things on TI-82/83's and the Winplot computer software.

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This page was prepared by Mary Parker, mparker@austincc.edu. It was last updated on January 14, 1998. The Web versions of the course materials are updated regularly. If you want handouts from previous semesters, those are still available from me.