Sarah Kitchen

Resources for Math 2250-1, Summer 2009:


: Syllabus
: Exam I Solutions
: Exam II Solutions

Maple Assignments

: Maple Project 1, Due Monday 6/15
: Project 1 Pictures (.mw)
: 6/2/09 Maple Demo for Project 1 (.mw)
: Maple Project 2 Due Thursday 7/2 (this is the correct due date -- the date on the actual pdf file is incorrect; campus is closed on Friday 7/3)
: 6/22/09 Maple Demo for Project 2 (.mw)
: Maple Project 3 Due Monday 7/20
: 7/10/09 Maple Demo for Project 3 (.mw)
: Maple Project 4 Due Wednesday 8/5 (typos corrected 8/2)
: Maple Demo for Project 4 (.mw)

Maple Tutorials and Resources

: To open .mws files, either save them to your computer and open them with Maple directly, or use the "Open URL" option in the Maple File menu. Clicking links labelled (.mws) will only give you gibberish.
: Getting Started with Maple, Tutorial from Indiana University
: Maple 12 Quick Reference Sheet, by Douglas Meade, USC
: Introduction to Maple 8-12 (.mws), by our own Angie Gardiner
: Introduction to Maple (.mws), by Nick Korevaar
: Maple Command List (.mws), by Nick Korevaar

Announcements:

(8/3) The average on Exam II was 71% ! Good job everyone -- it was not an easy test! Some comments:
- Most of the technical complications occured in the first three problems -- notably problems 1 and 3.
- Other trouble seemed to come from not knowing definitions, or becoming confused about definitions or what I am precisely asking you to do, and in many cases just not knowing how to start solving the problem. In this class there are many different problems where we use the same language in similar but non-equivalent ways to describe what is happening (e.g. characteristic polynomial for differential equations vs. matrices, or particular solutions for initial value problems vs. non-homogeneous differential equations). I *strongly recommend* coming to terms with this contextual use of language before the final, since we will be looking at the entire semester on the exam and will likely see similar language appear in drastically different problems.
(8/3) Comments about the final made in class today:
- The final exam will be 7-9 questions long (~1.5 hour test, but you will have the full 2 hour final period in which to take it).
- The final is cumulative, but at least 1/3 of the problems will be dedicated to Chapter 7 + Section 6.1.
- The Chapter 5 problems *will be similar* to those on Exam II (problems 1-3), so make sure you know how to do those problems! If you get a better score on these problems on the final, I will replace your scores on Exam II with them.
- Otherwise, study graded homework problems from the whole semester, all of the Homework #9 problems, and Exams I and II (solutions above).
- There will be an evening review tomorrow (Tuesday 8/4) at 6 pm, room LCB 215, and our usual problem session on Wednesday at 8:30 am, this week also in LCB 215.
- See previous announcements about important concepts for Chapters 1-5, 10. In chapter 7, big concepts to understand are,
  - Converting differential equations to systems and vice versa
  - Solving systems with the eigenvalue method (includes understanding how to compute eigenvalues -- see section 6.1, and defective eigenvalues in section 7.5)
  - Applications to coupled mechanical systems (2nd order) and tanks (1st order).
(7/22) I forgot to put below that you *will* get to use a 8.5x11 cheat sheet again (both sides) for the exam, but no calculators.
(7/21) The regular problem session this week will not be held at the usual time/place. To compensate for this, and to help you prepare for the exam, we will have two out of class review sessions:
- Wednesday 7/22 at 6 pm in room LCB 222
- Thursday 7/23 at 7:30 am in room LCB 215
If you can't make either of these sessions, but need/want help or have questions, please email me.
(7/20) Exam 2 is Monday 7/27. The material covered will be all sections of Chapters 5 and 10 for which you were assigned homework. As with the last exam, you should look carefully at the homework problems that were assigned -- all of them this time! The big concepts that are most important to understand are
- Solutions to second order linear homogeneous differential equations with constant coefficients -- specifically the use of the characteristic polynomial and the classification of the different types of pairs of roots that appear.
- Solutions to second order linear non-homogeneous differential equations with constant coefficients. Recall that the solutions to these equations are in two parts: the particular solution for the non-homogeneous equation, and the complementary solution to the underlying homogeneous equation. For the non-homogeneous equation, our primary approach to finding the particular solution was the method of undetermined coefficients.
- Applications of this type of second order equation! Specifically to harmonic oscillations (damped, undamped, forced, and free), and RLC circuits.
- Laplace transforms: The definition, computing transforms using the definition, solving initial value problems via Laplace transforms, and the computation of inverse transforms using the various tricks of sections 10.3 and 10.4.
Like last time, the exam will be 5-6 questions, and I will try to come ~5 minutes early and stay until 8:30 am, so you should be able to take your time with this one. We don't have time for an in-class review this week, but can potentially do an out of class review some time on Wednesday afternoon. We will determine the details of this review in class tomorrow morning. Any other questions/concerns/complaints/etc, email me.
(7/17) There will be a substitute on Monday. I will be on campus if you need me for any reason, but I am responsible for helping set up a math conference in my area (Representation theory) that morning during lecture.
(7/14) The class decided in lecture today to make Homework 7 due Friday 7/17!
(7/13) The due date for Homework 7 has been pushed back to Thursday 7/16. Also, note that section 3.7 and the assigned problems from this section can be found in the University of Utah custom supplement to the book (not in the book itself!). This section covers RLC circuits as an application of second order non-homogeneous linear differential equations.
(7/8) There will be a Maple demo for project 3 on Friday 7/10.
(6/30) I announced in class today that since I have been extremely rigid about homework and Maple project due dates, that I will drop the two lowest homework scores and your lowest Maple project score.
(6/20) Exam I info discussed in class on Friday:
- Exam I will cover chapters 1-4. You should study graded homework problems, starting with section 1.2 to prepare for the exam. Make sure you know how to do the graded word problems in particular, and the more practice you have with computational problems in general, the better prepared you will be. Graded problems from homeworks 1-4 are below. Homework 5 isn't due until after the exam, but you are still responsible for this material! Graded problems for this assignment aren't given below -- you should study all of them.
- There *will* be a subspace type of problem, similar to those covered in the chapter 4 homeworks. That means you *will* have to show something is a subspace and/or determine linear independence of a spanning set.
- *NO* calculators will be allowed on this exam, but you can bring one 8.5x11 sheet of paper with notes. No other books/notebooks/materials are allowed.
- I will come a little early to class so you can begin the exam at 7:25 am. Also, I will stay a little late so you can turn it in at 8:25 am. There may be a class using the room after us that day, so we shouldn't stay any later than this.
(6/16) The first exam is next Friday, 6/26. It will cover material from Chapters 1-4. More information and review materials will be made available on Friday 6/19. There will be an in-class review next Wednesday 6/24.
(6/8) Email me to let me know which problems you are having the most trouble with. Then, I will be able to email the entire class (this will go to your umail account unless you have set up forwarding) with suggestions for these problems, and I can come in early (~10 minutes before class) to address the most common concerns.
(6/6) A group of students will be meeting in the tutoring center about 6:10 pm on Monday 6/8 to work on Homework 3. Join them if you can, and if you can't but want to organize another student group, let me know and we'll make an announcement in class.
(5/6) Class begins Monday, May 18. Our classroom is LCB 215, except on Friday, May 22 when we will use room JTB 110.

Tentative Homework Schedule:

Assignment Due Date Sections Problems Graded Problems

Homework 1 (20 points) W 5/27
1.1
1.2
1.3
1.4

# 1-5 odd, 13,15,17-21 odd, 27, 31

# 3-9 odd, 11-15 odd, 23, 27, 29, 31

# 1, 5, 13-17 odd, 25, 27, 29

# 11-15 odd, 21-25 odd, 33-39 odd, 65, 69

# 3, 17, 27

# 5, 15, 29, 31

# 5, 13, 25

# 11, 25, 33, 37

Homework 2 (20 points) F 6/5
1.5
2.1
2.2

# 7-15 odd, 29, 31, 33, 37

# 1-5 odd, 9, 11, 15, 27

# 3-9 odd, 13-17 odd, 21

# 7, 13, 33

# 3, 5, 9

# 5, 13

Homework 3 (20 points) W 6/10
3.1
3.2
3.3
3.4

# 5-11 odd, 25, 27, 31, 33

# 13-17 odd, 21, 23, 27

# 3-9 odd, 23-27 odd, 35

# 3, 7, 9, 13, 17, 23, 29, 39

# 7, 25

# 13, 23

# 9, 25

# 3, 9, 17

Homework 4 (20 points) W 6/17
3.5
3.6
4.1
4.2

# 5, 7, 9, 13, 23, 25, 37

# 3, 9, 15, 23, 29, 35, 43, 45

# 1-21 odd, 29-35 odd

# 1-5 odd, 15-21 odd, 25, 27

# 13,23

# 3, 29

# 17, 31, 33

# 5, 15

Homework 5 (20 points) M 6/29
4.3
4.4
4.7

# 9, 11, 17, 23, 25

# 3, 5, 9, 13, 15, 19

# 1-17 odd, Optional/ungraded: 23-29 odd

# 11, 17

# 5, 9, 19

# 1, 7, 15

Homework 6 (20 points) W 7/8
5.1
5.2
5.3

# 9, 13, 17, 25, 26, 33, 39, Optional: 30, 31

# 7, 9, 15, 24, 27, Optional: 37, 39

# 5, 11, 19, 25, 33, 35

# 9, 17, 25

# 7, 15, 24

# 5, 19, 33

Homework 7 (20 points) F 7/17
5.4

5.5
5.6
3.7 (Supplement)

# 1, 3, 15, 19, 22

# 9, 13, 15, 18, 31, 41, 47, 51

# 1, 5, 8, 19, 26

# 1, 5, 7, 11, 17

ungraded

# 9, 15, 31

# 1, 8, 19

# 5, 11, 17

Homework 8 (20 points) M 7/27
10.1

10.2
10.3
10.4

# 1, 5, 7, 17, 19, 25, 31, 35

# 5, 10, 17, 23, 27

# 1, 3, 5, 7, 13, 27, 39

# 1, 5, 9, 17, 21, 25, 29, Optional: 35

# 1, 7, 19

# 5, 17, 23

# 1, 5, 13

# 2, 9, 25

Homework 9 (20 points) H 8/6
6.1

7.1
7.2
7.3

7.4
7.5

# 3, 13, 25

# 1, 5, 13, 19

# 5, 11, 15, 18

# 3, 9, 17, 26, 27

# 3, 9, 11, 13

# 5, 7, 25, 33

TBD