Problem 21 from section 13.3: I was asked about this, here is a complete solution
The worksheet
Worksheet with answers (Corrected 3/10/04! Thanks to the class for showing
me where I was wrong, and Brent in particular for leading me to the right
answer!)
After the exam:
Here is a copy of the exam
Here is a set of answers to the exam
Our first exam is Tuesday evening, February 24, from 7:15 to 9:15, in room
B337 Van Vleck. The exam will cover sections 8.1, 8.2, 8.3, 8.4, 9.3, 9.4, and
10.1 through 10.5 in the text. There are 8 problems on the test but most have
several parts. I distributed in class some additional problems on integrals and
on sequences and series that you might use in studying: You can now view here:
The series problems
My answers to the series problems
The integral problems
My answers to the integral problems
(The answers were done quickly and may contain either mathematical or
typographical errors: Please let me know if you think something needs
correcting!)
Math 222, the second semester in the mainstream calculus sequence at UW-Madison, covers several somewhat separated topics: There is not as much obvious connection between the topics as in 221, where essentially everything in the course can be described as coming from the concept of limit. (Limits themselves, the particular limit which gives rise to the derivative, applications of that, the particular limit which gives rise to the integral, and applications of that.) The course will include the following topics in this order:
In case you are taking this course but have not taken the previous course (Math 221) at UW-Madison, here is some of what we assume you know at the beginning of the course: Definitions of the derivative and integral as limits, and the ability to calculate derivatives and integrals (not necessarily using the limit definition) of various functions; How to apply derivatives to solve "story" problems involving related rates and finding maxima and minima of functions, and to assist in producing or analyzing graphs; How to apply integrals to solve problems involving area, some volumes, and the average value of a function; How to work with exponential and logarithm functions, trigonometric functions, and inverse trigonometric functions. You should be able to work with limits at infinity and limits which "are" infinity, including the use of l'Hopital's rule. Various theorems, notably the Mean Value Theorem and the Fundamental Theorem of Calculus, are important but will be valuable as tools to use rather than as abstract theorems or as statements to memorize. (All of these topics from calculus are covered in the textbook in chapters before the ones we will be studying, so if you need to review this material, it is available there.) You should also, from algebra, be able to solve a couple of linear equations in two unknowns, and perform elementary calculations with complex (imaginary) numbers. (The text has a chapter, chapter 17, on complex arithmetic: We won't cover this chapter in class, but if you need to review the topic that would be a good source. There is also an appendix which includes how to solve a system of linear equations using matrix methods, but you can also solve them using other methods for the little use we will make of this tool.)
The Mathematics Tutorial Program will be offering workshops "What Are You Expected to Know in Your Math Class?" at the beginning of the semester. These will include reviews of much of the material we expect as background necessary for success in 222. For details see their web site, http://www.math.wisc.edu/~tprogram/workshop.html.
Our textbook is Calculus, 8th edition, by Varberg, Purcell, and Rigdon: This is probably the same text you used for Math 221. There are places where this book could use a greater variety of problems but it is pretty readable.
You are welcome to use a calculator (including scientific and graphing calculators) in this class but you are not required to have one. All exam problems will be constructed so that they can be done without a calculator.
The order in which we will take up the topics is partly determined by making sure that important topics don't run the risk of getting squeezed at the end, but also by the desire to have chapters 13 and 14 fresh in your minds for those of you going on to Math 234. The schedule gives both reading assignments and suggested problems for you to do to check your understanding. The text also has "Technology Projects", the sections in blue at the ends of the chapters: You will not be required to learn the technologies (such as Maple or Mathematica software) to do these, but if you are interested in applications you should look at these and try some of them. I will be glad to help you with the technology, except that I can't pretend to be an expert on all possible versions!
Here is a schedule for the sections we will be covering, day-by-day throughout the semester. For each section there are problems listed: These are problems you definitely should try, as a calibration for how well you understood what you read and what was covered in class. I won't be taking up your answers to these problems but I will be glad to go over them either in or outside of class! (As of 1/13/04 I only have the problems listed for the first six weeks or so...)
Here is a course description with some information on how grades will be calculated.
I will have printed copies of both the schedule and the description at the first class.
Page visited
times since 1/13/04.