# MAT 253, Spring 2015

Welcome to Math 253, Calculus III. The syllabus is here. It contains information on class times, exam times, office hours, contact info, etcetera.
This website will be used to make announcements, post homework assignments, post practice exams and solutions, etcetera.

HW is due at the BEGINNING OF CLASS each Wednesday. (You may also put it in my mailbox in Fenton hall if you don't come to class, but then you'll miss the quiz.)

I will be absent the week of 4/6. Class will be taught by a substitute. My office hours are cancelled that week.

HW 1 (due W 4/8)

Reading: Section 8.1 and Appendix D pages A32-33
Section 8.1: 8, 10, 12, 16, 18, 20, 22, 25, 29, 31, 34, 41, 50, 51, 52
Appendix D: 21 (use Wolfram alpha), 22, 24

Suggested practice (DO NOT TURN IN): Section 8.1, the remainders from 3-34.

HW 2 (due W 4/15)

Reading: Section 8.1 on recursive sequences, Section 8.2, Section 8.3 except comparison test.
Section 8.1: 48, 54, 56
Section 8.2: 12, 14, 16, 20, 23, 24, 30, 33, 34, 36, 42, 50
Section 8.3: 2, 12, 14, 18, 23

Suggested practice: many many problems in section 8.2.

HW 3 (due W 4/22)

Reading: Section 8.3, Section 8.4 except ratio test.
Section 8.3: 9, 15, 17, 19, 28, 30, 33, 35, 38
Section 8.4: 4, 5, 9, 13, 14, 19, 27, 31

Here is the first practice midterm. Solutions are here.
HW 4 (due W 4/29)

Reading: Section 8.4 ratio test, Section 8.5.
Section 8.4: 15, 21, 22, 23, 29, 30, 33, 35, 36, 37
Section 8.5: 4, 5, 6, 7, 8, 9

HW 5 (due W 5/6)

Section 8.5: 10, 11, 14, 17, 23, 26, 33, 34
Section 8.6: 4, 6, 8, 9, 14, 17, 27, 28

Suggested: Make sure that you fully understand 8.5: 25 and 8.6: 1,2. They are easy conceptual questions, so long as you understand what is going on.

HW 6 (due W 5/13)

Section 8.7: 2, 4, 6, 8, 9, 11, 14, 15, 17, 22, 24, 26, 28, 30, 43, 46

Suggested: Pretty much every problem from 1 to 50 is good (except 19, 20).

HW 7 (due W 5/20)

Section 8.7: 19, 20 (these have to do with error estimation!), 39, 42, 49, 50
Section 8.8: 3, 4, 6, 11, 12, 13, 14, 21, 22, 24, 25, 26

Here is the second practice midterm. Solutions are here. (There was a sign error on a previous version of the solutions, in problem 5c. It is fixed now.)

Change of Schedule!! Homework 8 will be due Thursday 5/28 instead of the usual Wednesday. It will be posted by the end of the week. To hand in the homework on Thursday, place it in my mailbox, across from my office at Fenton 210, by 5PM. The Quiz will be on Friday 5/29 instead of the usual Wednesday.

Here is a scan of some chapters from the MAT256 textbook, on power series methods towards solving differential equations. This textbook is also in the library.
Here is a link to a free online ODE textbook and its chapter on power series methods. It may also be helpful to read their introduction to ODEs.
For both of these, really focus on following the examples. Some of the stuff in the text won't make sense without the background, but the examples are something I want you to be able to imitate.

HW 8 (due THURSDAY 5/28) ... but if you want a little more time, make sure it is in my mailbox by noon on Friday.

Reading: Chapter 5.2 from here or Chapter 7.2 from here. Also, practice recognizing common Taylor series being evaluated.
Section 8.7: 59, 60, 61, 64, 65
Chapter 5.2 from scan: 15(a), 16(a), 17(a), 18(a), 1(abd), 2(abd).

HW 9 (due THURSDAY 6/4) ... a short homework this week, assigned a little late (sorry!)

Chapter 5.2 from scan: 3(abd), 5(abd), 6(abd), 11(abd), 14(abd).
Crap! I didn't notice that the problems were worded the way they were. Here is some clarification. The number x0 that they give you is the center! In part (b) they ask about two solutions y1 and y2. Don't worry about that. What I want are the first four terms for ARBITRARY initial conditions, i.e. viewing a0, a1, or what have you as abstract variables.
Also, if you want to redo some of the problems from Chapter 5.2 from HW 8 that you got wrong, you will get credit.

Schedule for the last week and final week:
Tuesday: go over Midterm 2.
Wednesday: Additional review. Final list of topics is here.
Friday: Quiz! Additional review. Practice final is here.
Monday: Practice final solutions are posted here. I will hold office hours. Extra hours by appointment.
Tuesday: Office hours. Extra hours by appointment.
Wednesday: Extra office hours by appointment.

I just noticed a bad error in the (previous) solutions to the practice final. In problem 1(f), the value 7 is definitely not within the interval of convergence of the power series for ln(1+x). The series diverges (by a ratio test).

Another error was also noticed by a student. In 3(bc) I misread my own problem, and forgot about the extra 15. So a1 = 15 + 8a0 is correct. Consequently, the formula for a2 is wrong as well. So is the formula for the first three terms at the end. Sorry!

Both errors are now corrected on the solutions pdf.
Extra credit: confirm this.

Ben Elias
Department of Mathematics
Fenton Hall, Room 210
University of Oregon
Eugene, OR 97403
Phone: (541) 346-5629
Fax: (541) 346-0987
e-mail: bezzzzlizzzzas@uorezzzzgon.edu