Math 234, Fall 2005
9:55 MWF, B102 Van Vleck
Lecture 2, Wilson

CLICK HERE for the final exam with answers

(The exam, like other math files, is in Adobe PDF format. I have noticed that when reading them with some old versions of the Adobe Acrobat Reader program you may see lines across the page or boxes around some parts of a page. If you are seeing those you might want to update your version of the program, free at www.adobe.com.)

The final exam is 7:25-9:25 PM on Tuesday, December 20. Students in James Hunter's discussion sections will take the exam in room 22 of Ingraham Hall, all others in room B10 of Ingraham Hall.
CLICK HERE for a list of topics to review for the final.
There will be 10 problems on the final, 3 of which will be specific to Chapter 17. You are allowed to bring notes on up to 3 index cards (no larger than 4"x6") and you are allowed to use a calculator.

CLICK HERE FOR SECOND MIDTERM EXAM WITH ANSWERS

I sent an email to the class regarding a mistake in problem 28 on page 675 in the text. Click here to see the incorrect and correct equations set in mathematical type.

Concerning the first midterm exam:

Here is a set of answers to the exam. (The early, alternate, exam for those with conflicts, was slightly different.)

In the email I sent out re the first exam, there was a URL for my old calculus exams. To simplify things, HERE is a link directly to the calculus exam page.

Click here to see the list of topics for the exam, that I mentioned in class 10/5/05. (This is an Adobe PDF file, your web browser probably already has a program for reading it. If not, go to 

Click here to see a copy of the email I sent to the entire class regarding our first exam.

9/16/05: Several people have asked me to post the Maple code I used in class last Wednesday. That produced an animated plot traversing a curve, showing the position, velocity, and acceleration vectors. HERE is a link to a copy of that file: If you click on it you will probably get the option to save it to a file on your computer, or on a PC you can right-click on it and choose "Save Target as ..." to save it to your computer.

I have posted here the version I used: It can be improved a lot. In particular it defines the position function r(t) and then separately defines the velocity and acceleration, using what we know to be the right derivatives, rather than having Maple do the differentiating. When I get a chance I will improve that: Then one could easily change the curve without having to change also the velocity and acceleration calculations.

OK, a few hours later: I have changed this so it does the differentiations  itself. So now you can change the function r(t) to something other than  the helix I used in class and all will work fine... Except that it still will try to plot it in the same window, so if you use a function that goes off somewhere else you may not see much. But, for example you can change the line defining r(t) to
     r := t->[cos(t),t, sin(t)]; 
and the you will have a helix spiraling the opposite direction, or to
     r := t->[sin(log(t+1)),t, cos(t)];
and see what you get then!

From the beginning of the semester:

Math 234 is the third semester in UW-Madison's main calculus sequence. For the most part it takes concepts (derivatives, integrals, graphing and slopes, etc.) that have been studied in the first two semesters and moves them out of the plane: Previously a function was typically something like y=f(x) where x and y each represent a single real number. We will now allow them to have multiple components, so that x or y might represent a point in space, or a vector having direction as well as magnitude.

In connection with this course I have agreed to be part of the "Maple Adoption Program" arranged by the computer software company Maplesoft. Maple (presently version 9.5) is a powerful program in the category usually called Computer Algebra Systems. Maple and its competitors Mathematica and Matlab surely dominate this market, although I do not have statistical data on market share. I, personally, have been using the various Maple versions for many years now, but I also have used and occasionally still use those competitors. I will be using Maple in class for demonstrations, and frequently I also use it when working out exam problems, to check my answers, or to produce pictures to include in exams or class handouts.

If you are going on in the sciences, including the social sciences, you will quite probably want and even need to use software like this at some point. Each of those competing programs has its own particular advantages: I find Maple most resembles the way that mathematics and science and engineering classes express and use mathematics, so it seems easier to use in connection with what you learn in classes. In addition it is exactly what I will be using in class.