Here are the TAs for our lecture, glad to have finished
grading the final exams about 1:30 AM after grading straight through:
The final exam will be two hours long, 5:05 PM to 7:05 PM on Friday, December 21, 2001. We have been assigned 125 Agriculture Hall as the room for the final exam. Make sure you know how to find that room before the exam!
We have set up two review sessions to help you prepare for the final. The first is Friday, December 14, 7:00-8:00 PM, in B203 Van Vleck. The second is Wednesday, December 19, 7:25-8:25 PM, also in B203 Van Vleck.
I have written up pages on the topics to be on the final exam. Click HERE to see a description of the material we have covered, or HERE to see a list of the individual topics. (If your web browser causes problems viewing the list, click HERE.)
Your final grade will be based on the midterm exams, the grade from your
discussion section, and the final exam. The final exam will count 200 points.
Each of the midterm exams will count 100 points. (I was speaking with someone
the other day and said from memory each midterm counted 50 points. It should
have been 100.) The discussion grade will count 50 points. This gives a total of
550 points. After the final exams are graded we will make a "curve"
assigning letters A, AB, B, etc. to points on that 550 point scale.
We will make deviations from that scale to account for students who show on the
final exam they know material that they did badly on at the time of an earlier
exam. Otherwise the final grade will come pretty directly from this final 550
point curve.
I have added a couple more old exams to my on-line collection of old exams for Math 222, at http://outreach.math.wisc.edu/local/Courses/OldExams/Calculus.htm. There will not be a published "practice exam", but you can see old exam questions there and also at the Math Department's sample exam collection http://www.math.wisc.edu/~sample.
The first exam is Tuesday, October 2. It will cover the material from chapters seven and eight that we have done in class: If we skipped a section, according to the printed course schedule, that section will not be directly covered on the exam.
Since (a) you are allowed to bring in certain notes and (b) there are formulas which contain the effective result of doing several of the integration processes we have covered, but the exam should test whether you can apply those processes, there are specific instructions on what you are and are not allowed to use on integration problems. Those instructions, and the formulas they refer to, will be printed on the exam. So that you can prepare for the exam, they are also available at this web site: CLICK HERE. In order to put the mathematical formulas on the web I have used Adobe's Portable Document Format: If your web browser will not display properly the link above, you can download Adobe's free Acrobat Reader software here.
If you have been certified by the McBurney Disability Center for accommodation to a disability, please bring your "VISA" provided by McBurney to me by Wednesday, September 26. I will make arrangements to accommodate your needs. In this case your exam will probably be proctored by the Math Department's Tutorial Program: I will make arrangements with them for some things, but you will also have to meet with the Director of the Tutorial Program (David Camacho, camacho@math.wisc.edu) and show him your VISA.
If your TA is Neil Lyall, Clark Good, or Aaron Greenblatt, and you are
taking the regular 5:30-7:00 exam, go to room B102 Van Vleck. This is
the other large lecture hall in Van Vleck, NOT the room where we have
lecture.
If your TA is Prabu Ravindran, Sharib Haroon, or Jue Wang, and you are
taking the regular 5:30-7:00 exam, go to room B130 Van Vleck. This is
our regular lecture room.
If you are taking the conflict exam, 4:00-5:30, go to room B235 Van Vleck
no matter who your TA is.
Our second exam is next Tuesday, November 6 at 5:30. The schedule is the same
as for the first exam:
If your TA is Neil Lyall, Clark Good, or Aaron Greenblatt, go to room
B102 Van Vleck. This is the other large lecture hall in Van Vleck, NOT
the room where we have lecture.
If your TA is Prabu Ravindran, Sharib Haroon, or Jue Wang go to room
B130 Van Vleck. This is our regular lecture room.
The situation regarding conflicts or special (McBurney) exams is also the
same as last time: IF YOU CANNOT TAKE THE EXAM AT THE SCHEDULED 5:30-7:00
TIME, YOU MUST MAKE CONTACT WITH ME TO MAKE ARRANGEMENTS. Do not expect
to show up for a conflict exam without prior arrangements, and do not
expect to take the exam with extended-time or other special provisions
without arranging that with me! Anyone who has not made such arrangements
by noon on Friday, November 2, will be assumed to be taking the exam at
the regular time in the room detailed above.
Additional Differential Equation Problems: Here are some additional problems to try. And here are some answers. These answers were written up very quickly and might have typos, but they are basically right. They include comments on how to do the problems, not just the final answers.
Email sent to the class on 10/26:
I have in class defined and used a term which it is now pointed out to me is not printed in our (ancient) textbook. It is the standard terminology
and we should use it.
Given a differential equation, we may have with it initial conditions which specify which among infinitely many solutions is required. The
initial conditions are things like "y(1)=2 and y'(0)=3" to go with the differential equation.
An initial value problem (IVP) is just a differential equation together with initial conditions.
Our text introduces the term "initial conditions" back in chapter 4, and apparently never uses the term "initial value problem". I did define both
of these when we started chapter 18 but wanted to remind you of them now.
For example, y'' + y = 0 is a differential equation. All of the functions
y = C1 cos(x) + C2 sin(x) for all numbers C1 and C2 are solutions of this
equation. We could add y(Pi/2) = 2 and y'(Pi/2) = 1 as initial conditions
to form an initial value problem. The the only solution would be
y = -cos(x) + 2sin(x), i.e. C1 = -1 and C2=2.
Click here to see a list of the names of students taking the third exam at a different time because of a conflict. If your name is not on this list I do not have you scheduled for a conflict exam!
I have written up some additional notes and problems on using Taylor's theorem to estimate the error in approximating a function using a polynomial. This is the material of section 16-9 in our text, which does not have much explanation or enough different problems. Click here to read these notes and problems.
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: The workshops
on background for Math 222 are:
"Integration", Wednesday, September 5, 4:30-5:30,
B130 Van Vleck
"Derivatives, Inverses, and Substitution",
Thursday, September 6, 4:30-5:30, B130 VV
"Limits", Tuesday, September 11, 4:30-5:30, B130
Van Vleck
Our textbook is Calculus and Analytic Geometry, 5th edition, by Thomas and Finney. This is an older book which has been reprinted for use at UW-Madison by Pearson Custom Publishing. There is also a Student Solutions Supplement available: This is not essential for the course. The main text contains answers for many odd-numbered and a few even numbered problems, and the supplement contains more on how to get those answers. This text does not have as wide a variety of problems as I would like: Those of you who have access to a copy of the text we used before this one, the 3rd edition of Stewart's Calculus, or to another recent calculus book, might find it worthwhile to look at the examples and try some of the problems from that book. You can never do to many problems...
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.
I have a schedule for the lectures available on-line. 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 chapter 11 fresh in your minds for those of you going on to Math 234: It will start with the latter part of the chapter 11 material. The schedule gives both reading assignments and suggested problems for you to do to check your understanding.
A course description including how grades will be determined is available on-line also. I will have printed copies of both the schedule and the description at the first class.
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