Sections DA, DB
Timothy Carrell
Sections DC, DD
Bharathwaj Palvannan
Midterm 1: Tuesday, April 26
Midterm 2: Tuesday, May 17
Final Exam:
Saturday, June 4
1:30-4:20 PM
Kane 220
Course grades are now posted on Catalyst. These are the actual grades I will be sending to the registrar, so they include the course curve.
Have a good summer!
Here are the final exam stats: n=148; min=19; 1st quartile=71.75; median=87.5; 3rd quartile=94; max=100 (8 students).
Course grades have not been calculated yet. Catalyst will be updated as soon as they are done.
Graded final exams will be viewable during an office hour on Friday, June 10, 1-2 PM. Scores will be added to Catalyst today or tomorrow. Final exam can also be seen any time during Autumn quarter.
As part of your study for the final exam, you might make use of old final exams, which are available here.
Here is a review sheet for the final exam.
In lecture today, we worked out the Taylor series for the antiderivative of ex2.We then used this to give a series representation for the integral of ex2 from 0 to 1, and I said one could just sum up the first bunch of terms from that series to get an approximation of this integral. Here is a table of the results of that sort of calculation:
| number of terms | sum |
| 0 | 1.0000000000000000000 |
| 1 | 1.3333333333333333333 |
| 2 | 1.4333333333333333333 |
| 3 | 1.4571428571428571428 |
| 4 | 1.4617724867724867724 |
| 5 | 1.4625300625300625300 |
| 6 | 1.4626369001369001369 |
| 7 | 1.4626501276501276501 |
| 8 | 1.4626515865670277435 |
| 9 | 1.4626517316055499750 |
| 10 | 1.4626517447280829388 |
| 11 | 1.4626517458173050425 |
| 12 | 1.4626517459008120704 |
| 13 | 1.4626517459067598644 |
| 14 | 1.4626517459071554074 |
| 15 | 1.4626517459071800757 |
| 16 | 1.4626517459071815240 |
| 17 | 1.4626517459071816043 |
| 18 | 1.4626517459071816085 |
| 19 | 1.4626517459071816087 |
| 20 | 1.4626517459071816088 |
You can see that even with only 10 terms we get pretty good accuracy, and 20 terms gives very good accuracy. The Taylor idea is that we can get the accuracy to be as good as we need just by taking enough terms.
The example at the end of Wednesday's lecture was rushed. Here is a writeup with two similar examples. Let me know if you have questions about them.
Statistics for the second midterm exam:
min=6; 1st quartile=36; median=43; 3rd quartile=48; max=50 (18 students).
Estimated current grades will be posted to Catalyst later this week, so a 4.0 conversion table for this exam will not be posted.
Here is an argument for why (xn)/n! goes to zero as n goes to infinity, for all x. This argument is needed for concluding that the Taylor series for certain functions converge to the function for all x.
Answers to midterm 2 are now in the exam archive (link at right).
There is a bug in the coding for one of the Taylor webassign problems. For problem 2 of section 1, the second part of the problem is incorrect in some randomizations, so don't worry about doing this part. Everyone will get a free point.
The material in these notes supports our discussion of Taylor polynomials and series.
Please bring a copy of this handout to quiz section on Thursday.
Here is a review sheet for the second midterm exam.
Here is set of review problems; you can skip problems 12 and 13, as we will cover this topic after the exam. Here is a set of answers for these questions.
Answers to the first midterm exam are now in the archive (link at right).
Statistics on the first midterm exam: n=157; min=5; 1st quartile=30; median=38; 3rd quartile=44; max=50 (8 students).
The following is a table to help you interpret your exam score. This is entirely approximate: I make no use of these grade equivalents: it is just for you to get an idea of how you did, on a 4 point scale.
| exam score | approximate 4.0 equivalent |
| <25 | 0.0 |
| 25 | 0.7 |
| 26 | 0.8 |
| 27 | 0.9 |
| 28 | 1.1 |
| 29 | 1.3 |
| 30 | 1.5 |
| 31 | 1.6 |
| 32 | 1.8 |
| 33 | 2.0 |
| 34 | 2.2 |
| 35 | 2.3 |
| 36 | 2.5 |
| 37 | 2.7 |
| 38 | 2.9 |
| 39 | 2.9 |
| 40 | 3.0 |
| 41 | 3.1 |
| 42 | 3.2 |
| 43 | 3.3 |
| 44 | 3.4 |
| 45 | 3.5 |
| 46 | 3.5 |
| 47 | 3.6 |
| 48 | 3.7 |
| 49 | 3.9 |
| 50 | 4.0 |
A review sheet for midterm 1 is now available (link at right).
Dr. Taggart, who teaches another section of 126, has created a list of practice problems plus answers that you might find useful for studying.
Some of those problems may overlap with problems from my old exams, which are all available via a link at right.
A handout on quadric surfaces is not avilable in the right-hand column.
A new handout on lines and planes has been added to the right-hand column. One of the examples addresses how to find the distance from a point to a plane.
As a partial summary of our study of line and planes in 3D, the following is a list of things you should be able to determine or find.
The course discussion board is now availble (link at right). Please take advantage of it to ask questions about homework problems or course topics. You might also use it as a way to arrange study groups. I will get immediate emails when posts are added to the board, so this is as good a way to contact me as email, but allows everyone to see my response.
Welcome to Math 126D.
Announcements and other important information will appear here, so check back frequently.
The homework for this course will be on WebAssign.
Here is the link to the login page for WebAssign.
Here is a jpg with instructions on how to log in.
The first homework assignment will be due on April 5.
Dr. Conroy's 126 Exam Archive
Course Syllabus (pdf)
Course Discussion Board
Math 126 Materials Website
Math Study Center
Student Counseling Center
Information for Students of International TAs
Center for Learning
and Undergraduate
Enrichment (CLUE)