Calculus is the mathematical study of change. In this course, we will first look at the derivative, which is the instantaneous rate of change. Not the average rate of change over 10 years or 10 months or 10 minutes or 10 nanoseconds, the rate of change at this very instant! We'll examine tools for analyzing the rate of change and how knowing the rate of change can give us information about maximum values, minimum values, and various physical applications. We'll also study another aspect of rates of change, namely that of accumulated change. For instance, you probably all remember from high school that the distance I travel in my car can be computed by multiplying the speed (or rate) at which I'm driving times the time I drive. However, what happens if my speed varies over time? Suppose I start out at Georgia Tech and want to drive home to Fargo, North Dakota. If I drive a constant speed, you know how far I've travelled if you know how long I've been on the road. But what if I slow down to five miles per hour under the speed limit every time I see a state patrol car, stop five times to fill gas, and spend the night in Illinois? My car's speed is then changing, and changing often. If you know my instantaneous speed for any moment in time, can you compute how far I've travelled after 10 hours? In fact, you can, and in this course we'll learn about integration and how it can help solve this problem and many others.
Why should you study calculus? Well, for most of you, it's probably required for your major here at Georgia Tech. However, it's really far more important than that. In this course, you'll learn how to approach problems and think logically. You'll also see tools that have been used by physicists, chemists, biologists, epidemiologists, economists, engineers, and mathematicians for centuries to advance their fields. Without the foundations of calculus, science and engineering would not be where they are today, and in order to be successful in those fields, you really will need to have an understanding of the mathematics that underlies it all.
This course is taught in the lecture-recitation format at Georgia Tech. This means that three days per week, over 120 students will meet with me in a lecture hall. In these sessions, I will present new concepts and work examples for you to learn from. To prepare for lecture, you should consult the online schedule and see which section(s) from the text I will be covering the next day and read over them in advance. You won't necessarily understand everything just from that first reading of the text, but it will give you a foundation on which the lecture will build. (You don't need to bring your textbook to the lecture with you if you don't want to.) Unfortunately, because of the size of the class, it will be hard for this class to be very interactive. However, I'm going to do my best and I want your help. Don't be afraid to ask questions or point out if you think I've made a mistake. If you've got a question, it's likely that 10 other students do as well, so please ask it. I'll do my best to answer it within the time constraints we have. Also, if I ask a question to the class, don't be afraid to answer it! Fortunately, on Tuesdays and Thursdays you will meet with a teaching assistant (TA) in a smaller group, which is really your chance for interaction. Your TA will answer any questions you had about the lecture(s) since your last recitation and will help you work homework problems, so you need to try the homework problems before recitation. You will also take quizzes in recitation (more on that later). Please note that attendance at both lecture and recitation is imperative. It will be hard to succeed in this course if you don't attend both.
The formal prerequisite for this course is completion of MATH 1113 (Precalculus) with a grade of D or better or an SAT Math score of 550 or higher. What does this mean in practice? You need to be able to add fractions. You need to be able to compute things such as (-2)-3 quickly in your head. You need to be able to factor polynomials of small degree. You need to know that (x+y)2 is x2 + 2xy+ y2 and not anything else. You need to understand the composition of functions. For example, if f(x)=x+3 and g(x)=1/x, f(g(x))=(1/x) + 3 while g(f(x)) = 1/(x+3). (This is essential! We will compose functions all the time in this course, and you need to be able to do it like a pro.) You need to know the values of sine and cosine at fundamental angles (0, π/6, π/4, π/3, π/2, π, etc.). You need to know a few basic trig identities such as sin2θ+cos2θ =1. You need to know what the graphs of y=7x-4 and y=x2 (among others) looks like. You really should be comfortable with logarithms and exponentials, at least their basic properties. For example, log(ab)=log(a) + log(b). We'll spend a bit of time on logarithms and exponentials later in the course, but if you're familiar with them already, it's going to go a lot more smoothly. Section 5.2 of Adams, Thompson, and Hass gives a pretty good summary of what you should know, as does most of Chapter 1 of Salas, Hille, and Etgen. (We'll talk about 1.8 in class, but you should already have the rest down cold.)
If you're unsure if you're ready for this course, please come see me before the end of the first week of class. I want all of you to succeed at Georgia Tech, and part of success is being prepared for the classes you take.
Back to MATH 1501G1/G2/G3 homepage
Disclaimer: This page and the associated web site is not a publication of the Georgia Institute of Technology and the Georgia Institute of Technology has not has not edited or examined the content. The author of the page is solely responsible for the content.
|
|
|
|