The Math 126 Materials Website lists the textbooks, the course schedule, the calculator policy, and a note of advice for students. Note on the texts: For the Stewart Calculus, you may use just the "second half" version, starting with chapter 10. You must print your own copy of the supplemental Taylor Notes. If this is your first math class at UW, be sure to read the "note to students."
See the
Math 126C Homepage and the links thereon for information about
instructors, their offices and office hours, classwork,
tests and quizzes, homework, and the grading system for
the course. Be sure to read the following.
"Office hours are part of the course" on the
Office Hours page;
"Important comment on group work" on the
Worksheets and activities, quizzes, and tests page;
and "The importance of doing all the homework cannot be overemphasized"
on the
Homework and study suggestions page.
Math 126 is probably different from your previous calculus classes in several ways. One is the variety of topics included. You could title this course "All the things you ought to learn in first year calculus that we didn't cover in 124 and 125." We start with two weeks on Taylor polynomials and Taylor series, from notes written for this topic. Next, Chapter 12 in the Stewart text introduces vectors and ways to describe and work with lines, planes, and other surfaces in three dimensions. This chapter has no calculus in it, but serves as background for doing calculus in higher dimensions. In Chapters 10 and 13, we study curves in two and three dimensions. That is, we look at calculus for functions that have one independent variable and two or three dependent variables. In Chapters 14 and 15, we start the study of calculus for functions that have two or more independent variables and one dependent variable. In each of these chapters, we just do an introduction to the material. (You should continue on to Math 324 to get the real story on this topic. The reason we do a bit of each chapter instead of all of one is that some majors require Math 126 but not 324, and need a little bit from each of the chapters.)
Many students find the Taylor polynomial and series material significantly harder than previous calculus material. There are two goals in this section of the course. One is for you to learn some basic facts and techniques for manipulating Taylor polynomials and series. Even these facts and manipulations involve a bit more abstraction than most of Math 124 and 125. The second goal is to learn about bounding the error that may occur if we use a Taylor polynomial to estimate values of a function. If you are going into science or engineering, you may often use numerical techniques that produce an estimate rather than an exact answer. Typically, there's some kind of repetitive calculation done to make the estimate, and there's an error bound that decreases as the number of repetitions increases. In this course, the "Taylor Inequality" gives an example of this kind of error bound. Even if you are not interested in error bounds for numerical calculations, the error bound problems are important for a second reason. Finding the bound is a multistep process, and the answer is not just a number but also the reasoning behind the number. Learning to do this kind of multistep reasoning is one of the primary goals of taking mathematics.
The rest of the course presents a different kind of challenge: working in three dimensions, and learning to use all kinds of algebra (precalculus) and differential and integral calculus there. So we have the difficulty of visualizing and working with three dimensional objects, and of going through many of the topics you did in 124 and 125 for one variable calculus (all in part of a quarter).
At this point you are probably wondering, "If this course is so challenging, why do we switch to larger classes at this point?" The answer is, as a student who has successfully completed Math 124 and Math 125, you are a mature mathematical learner! We are counting on you to have learned to read and learn from the book; to prepare for class so you can ask questions in class (even in lecture!); to realize that problems may take a long time to work; to try problems early so you can work on them, come back again later, get help, and still try again before the homework is due; to know when you have the basic idea and when you need to ask for help; and to seek out help when you need it, in the MSC, office hours, in other books or websites, etc.
How to get the most out of lectures. The topic for each lecture is listed on the Math 126 Materials Website. You will learn more from lecture if you look over the topic before coming to class. When you arrive at lecture, check the board for announcements. Do ask questions in lecture. If you come to lecture with questions, it is helpful if you write them down, one question on each sheet of paper, and give it to me before class. If you have discussed the question with others in the class, indicate how many people have the same question. (If there are more questions than time, I concentrate on questions or topics most asked about.) Finally, if you can't hear, or can't read my writing, or don't know the definition of some word or symbol I'm using, speak up right away!
Lecture Courtesy: Please be on time for class. Please do not get up and leave in the middle of lecture; you are neither invisible nor inaudible, and you do disrupt both the lecturer and the other students. If for some special reason you must leave one lecture early, please sit on the aisle near the door and leave as quietly as possible. (I do not insist that you tell me before lecture why you will be leaving early, but be aware that some faculty feel that it is only common courtesy that you do so.) Please do not start zipping up your bag and other preparations for leaving until the end of class. Please turn off your cell phone and the alarm and hourly chime on your watch. (You may hear my watch alarm, warning me when to wrap up my lecture so I can end on time.)
Return to the Math 126C Homepage.