Justin Tittelfitz
jtittelf at math.washington.edu
Midterm 1: April 21
Midterm 2: May 14
Final Exam:
Saturday, June 6
1:30-4:20 PM
Johnson 175
Here is the updated grade record with the third writing problem, final exam scores, and course grades.
By the way, I could really use more writing problem samples. Either electronic (you can email me them) or not (you could envelope them and place them in my mailbox or under my office door), and either anonymous (i.e., you can leave your name off) or not. I think it would be a big help to future students, and I'd really appreciate any contributions.
Have a good summer!
Finals are graded. Here are the scores:
57,59,71,71,74,76,81,81,81,82,83,84,86,86,86,87,87,89,90,91,91,92,93,93,93,93,95,95,96,97
Stats: n=30; min=57; 1st quartile=81; median=86.5; 3rd quartile=92.75; max=97.
I still have to grade the last writing problem, then I'll update the grade record with all the scores and course grades.
I will be holding an office hour from 2 to 3 PM this Friday, June 12, for anyone who would like to see their final exam. I hope to update the grade record with final exam scores and course grades by then.
I will keep the final exams for several quarters, so if you cannot make this hour, but would like to have your exam, you can stop by in the fall.
Here is a study guide for the final. Let me know if anything is unclear.
Here is the grade record.
If you find any errors, please let me or Justin know right away.
Here are a couple of examples of finding intervals with required error bounds.
Also, answers to the latest midterm exam are now posted in the exam archive, linked at right.
Here is Writing Problem 3. Let's say it's due June 3.
Here is an applet illustrating Taylor polynomials of sin x.
The midterm on Thursday covers specifically sections 13.3, 13.4, 14.1, 14.3, 14.4, 14.7, 15.2 and 15.3.
In preparation for the second midterm, keep in mind that the homework problems are the foundation: you should be comfortable solving all of those. If you are, then the problems below are good extra practice.
There is a typo on the writing problem. The line
xy = ey ln x
should read
xy = ey ln x
I will correct the pdf this afternoon.
Here is Writing Problem #2.
We've got a worksheet for this Tuesday. Please bring a copy of the worksheet with you on Tuesday.
I have added midterm one solutions to the archive.
Here are the scores from the first midterm:20,22,26,26,27,29,29,32,32,34,35,35,36,39,40,40,40,42,43,45,45,47,48,48,48,49,49,49,50.
As you can see, the range is quite large. Certainly anyone who scored below 30 ought to be a bit concerned, with more concern appropriate the farther below 30 one scored.
Here is an animation of the curve x=t cos t, y = t sin t, z=t that I mentioned in class today.
There were a couple of errors in the solutions to the old exams. I have updated Spring 2006 Midterm 2 Problem 1, and Winter 2006 Midterm 2 Problem 3.
Here is a review sheet for the first midterm exam.
In the list of suggested problems below, I have made some of them red. These are the ones I'd like us specifically to discuss on Monday. Time and interest permitting, we can talk about other things instead/also.
Here are some comments on the "tangent spiral" I mentioned in lecture on Wednesday.
The homework schedule has been updated with some problems from sections 10.3 and 13.2 which you should do in preparation for the midterm exam on Tuesday.
The following problems on the old midterms available at right are worth studying for the midterm on Tuesday:
I've written a short comment about quadric surfaces (specifically cones, and hyperboloids) here.
Writing Problem #1
The three conic sections can be defined as follows.
The ellipse is the set of points P in the plane such that the distance r1 from P to a fixed point A1 and the distance r2 from P to a fixed point A2 satisfy the equation r1+r2=k for some constant k.
The hyperbola is the set of points P in the plane such that the distance r1 from P to a fixed point A1 and the distance r2 from P to a fixed point A2 satisfy the equation |r1-r2|=k for some constant k.
The parabola is the set of points P in the plane such that the distance r1 from P to a fixed point A1 and the distance r2 from P to a fixed line L satisfy the equation r1=r2.
What kind of objects do these definitions define in three-dimensional space? That is, if we consider points in three dimensions, and remove the phrase "in the plane" from the definitions above, what sort of object is defined? In all cases, we'll have a surface. What is that surface like? Can you give cartesian equations for these surfaces? Can you classify them? Are they quadric surfaces? Are they cylinders?
For this writing problem, give a thorough analysis of these surfaces.
Due April 17.
The following is a partial list of useful skills related to lines and planes in 3D.
You should be able to determine of find:
A number of the techniques needed to solve problems of the sort in 12.5 build on each other. For instance, in lecture we discussed how to find the distance from a point to a plane.
With that method, we can then find the distance between two parallel planes by simply choosing a point on one of the planes, and finding the distance from that point to the other plane.
If we have two skew (non-parallel, non-intersecting) lines, we may want to find the distance between them. The first observation to make is that, for any two such lines, are planes containing them which are parallel (that is, if the lines are l1 and l2, there are planes p1 and p2 such that p1 and p2 are parallel, and p1 contains l1, and p2 contains l2). One way to see this is to imagine fixing line l1. Then imagine moving l2 parallel to itself until it hits l1. The plane containing l1 and this shifted l2 is the one we want: it contains l1 and is parallel to l2. Do the same for l2: shift l1 parallel to itself until it hits l2; the plane determined by l2 and this shifted l1 contains l2 and is parallel to l1. The planes thus determined are parallel to each other. The distance between these planes is the shortest distance between the lines.
Section 12.6 in the homework is postponed until next week since I decided to spend two lectures on 12.5.
Welcome to Math 126 C, Spring quarter 2009.
Announcements and other useful things will be posted here during the quarter, so check this site frequently.