Instructor:

Dr. Matthew Conroy

Office hours and email

TA:

Lindsay Erickson
lae241 at
math.washington dot edu

office hours:
W 4-5 in PDL C-8-D
Th 1-2 in MSC


Exam Dates

Midterm 1:
Tuesday, April 20

Midterm 2:
Thursday, May 13

Final Exam:
Saturday, June 5
1:30-4:20 PM
CDH 135

June 10, 2010

Course grades are now available on Catalyst. These are the grades I will be reporting to the registrar.

June 8, 2010

Final exam stats: n=33; min=39; 1st quartile=67; median=73; 3rd quartile=82; max=87 (out of 90)

June 8, 2010

UPDATE: My office hours this Friday will be 12-2 PM.

June 5, 2010

I will be holding an office hour on Friday from 12 to 2 PM if you would like to stop by and see your final exam. I will most likely have course grades calculated at that time.

Have a good break!

June 2, 2010

Here is a review sheet for the final exam.

May 25, 2010

Answers to some Taylor homework problems can be found here.

May 24, 2010

Writing problem #3:
Let f(x) be a function and I be an interval around 0. Suppose f and all of its derivatives are defined in the interval I.
(a) Show that if f is even, then the Taylor series for f consists only of even terms, and if f is odd, then the Taylor series for f consists only of odd terms.
(b) Use Taylor series to (formally) show that
ei θ = cos θ +i sin θ
where i is the base of the complex numbers, so i2=-1. Conclude the famous identity
ei π=-1.

Due June 4.

May 21, 2010

Here is an applet I wrote to illustrate Taylor polynomials of sin x.

May 18, 2010

We are now starting the Taylor Series portion of the course. Instead of using the textbook, our work will be based on these notes. I will endeavor to make the lectures as complete as possible, but these notes will be available to fill in gaps and give you more examples and other perspectives on the concepts.

May 16, 2010

Stats for the second midterm: n=33; min=27; 1st quartile=39; median=46; 3rd quartile=49; max=50 (7 students)

May 10, 2010

Here are some suggested problems for study from my exam archive:

Also,

May 7, 2010

Here is a review sheet for the upcoming midterm exam.

April 26, 2010

David asked a good question today: how do we know that the acceleration vector is in the same plane as the unit tangent and unit normal vectors?
This hinges on the fact that the acceleration vector is a linear combination of the unit tangent and unit normal vectors.
In general, if a vector a is a linear combination of vectors b and c, then we can show that a is in the same plane as b and c. How do we do this?
One way is to show that a is orthogonal to b x c. We do that by letting
a = m b + n c.
Then we write
(m b + n c) dot (b x c) = m b dot (b x c) + n c dot (b x c) = 0
this last due to the fact that a scalar multiple of a vector is orthogonal to any cross product involving that vector.
Now, we need to show that the acceleration vector is a linear combination of the unit tangent and the unit normal vectors.
We did this in class with a fancy equation that explicitly showed that linear relationship.
More directly, we might do this. We know
T(t) = r'(t)/|r'(t)|=r'(t)p(t), for a scalar function p(t), say,
so T'(t) = r''(t)/|r'(t)| + r'(t) k(t) for some scalar function k
(differentiating T(t) is kind of a pain, but this is all we need to conclude about T'(t) for now).
So then N(t) = T'(t)/|T'(t)| = r''(t) m(t) = r'(t) n(t), say, where m(t) and n(t) are some scalar functions.
So, we've shown that T(t) = r'(t) p(t), and N(t) = r''(t)m(t)+r'(t)n(t)
but r''(t) is the acceleration vector, so rearranging we can write r''(t) as a linear combination of N and T,
and so the acceleration vector must be in the same plane as N and T.

Whew!

April 21, 2010

The writing problem is now due on Monday, April 26.

April 17, 2010

All of Spring 2009 (in the archive at right) is worth examining in preparation for Tuesday's midterm.

In addition, the following problems on the old midterms available at right are worth studying:

April 15, 2010

Here is a short review sheet for midterm one.

April 12, 2010

Writing Problem #1: Give a thorough analysis of the polar curves
rn = sin m θ
and
r = (sin mθ)n
where n and m are positive integers.

Some of these curves are referred to as "roses".

This applet displays some of these curves, plus others.

April 7, 2010

As a sort of summary of our beginning discussion of 3d geometry, here is a list of things you should be able to determine or find:

March 26, 2010

Welcome to Math 126C.

Announcements and other important information will appear here, so check back frequently.

Resources:

Homework Schedule

Dr. Conroy's 126 Exam Archive

Course Discussion Board

Math 126 Materials Website

Other UW resources:

Math Study Center

Student Counseling Center

Information for Students of International TAs

Center for Learning
and Undergraduate
Enrichment (CLUE)