Department of Mathematics

MATH 2250, Section 004, Fall 2008
TTh 12:25-2:10PM, JWB 335 (John Widtsoe Building)

Differential Equations and Linear Algebra

Instructor:

 Damon Toth
LCB 315 (LeRoy Cowles Building)
tel: 585-7657
fax: 581-4148
toth[at]math[dot]utah[dot]edu
Office Hours:
W 4:30-6:00PM
Th 10:00-11:30AM
(I am also available TTh right after lecture, or by appointment via email)

Teaching Assistants:

 Adam Gully & Shang-Yuan Shiu
gully[at]math[dot]utah[dot]edu
shiu[at]math[dot]utah[dot]edu
TA Help Sessions:
W 3:05-3:55PM, LCB 121
Th 7:30-8:20AM, WEB 103
Th 8:35-9:25AM, JFB 103

Course description Prerequisites Textbook Syllabus Schedule Grading Resources

Course Description

This course serves as an introduction to differential equations and their application to problems in science and engineering. Traditionally, a course in linear algebra is needed as a prerequisite to a differential equations course. For this course, no such prerequisite is needed, as linear algebra concepts and techniques are introduced as necessary before their application to differential equation problems. We will learn how to use differential equations to describe physical phenomena in mechanics, electrical circuits, population dynamics, and other areas. We will learn how to find, represent, and interpret solutions to differential equations exactly or approximately using a variety of conceptual and computational techniques. By the end of the course, students should be ready for more advanced courses in either differential equations (ordinary and partial), linear algebra, or scientific computing.

Prerequisites

Students should have completed Calculus I, II, and III before enrolling in this class. There are three different course sequences at the University of Utah that cover the necessary prerequisites - if you have successfully completed ONE of these sequences you are ready for this class. Sequence A: MATH 1210, 1220, and (Math 2210 or PHYS 2210 or 3210). Sequence B: MATH 1250 and 1260. Sequence C: MATH 1270 and 1280.

Textbook

Differential Equations and Linear Algebra, Second Edition, by Edwards and Penney

You may also purchase the Custom Edition, which is the same as the 2nd Edition but also includes the Student Solutions Manual bound at the back, which you may find useful. The course will follow the book fairly closely, and homework problems may be assigned from the book.

We will also be covering some supplementary sections by the same authors that will not be included in your book. If you buy a new version of the text from the bookstore, you will be able to download these extra sections using an access code. Otherwise, you will be provided with hard copies as a handout.

Syllabus

Main topics of the course: In the textbook, we will attempt to cover most of Chapters 1-10. Chapter 10 will be covered out of sequence (between Chapters 5 and 6).

Schedule

Assigned Date Due Date Homework Problems / Handouts
First day of class Tues. Aug. 26 CourseInfo.pdf
Homework #1 Thurs. Aug. 28 Thurs. Sep. 4 1.1: 4, 12, 20*, 24*, 34
* = graphing not required

1.2: 2, 8, 10, 18, 30

1.4: 2, 6, 12, 20, 34, 38, 48
Homework #2 Thurs. Sep. 4 Thurs. Sep. 11 1.5: 2-24 even, 34, 36

Computing Portion: HW2Computing.pdf
(helpful files below under Resources)

Homework #3 Thurs. Sep. 11 Thurs. Sep. 18 2.1: 6*, 10, 28
* = graphing not required

2.2: 2-12 even
(explicit solution & graphing not requ.)

Computing Portion: HW3Computing.pdf
(helpful files below under Resources)
Homework #4 Thurs. Sep. 18 Thurs. Sep. 25 3.1: 6, 8, 12, 20, 28

3.2: 2, 10, 22, 24, 28

3.4: 2, 8, 14, 20

3.5: 4, 6, 12, 22

Computing Portion: HW4Computing.pdf
(helpful files below under Resources)
Midterm 1 (in class) Thurs. Oct. 2 Midterm1Solutions.pdf
Homework #5 Thurs. Sep. 25 Thurs. Oct. 9 3.6: 2, 6, 8, 26, 28

4.1: 6, 8, 10, 18, 20, 26, 30, 36

4.2: 2-16 even

4.3: 2, 8, 10, 14, 18, 20, 24
No Class (fall break!) Tues. Oct. 14
No Class (fall break!) Thurs. Oct. 16
Homework #6 Thurs. Oct. 9 Thurs. Oct. 23 4.4: 2-16 even, 24

4.7: 6-16 even, 24

5.1: 4-12 even, 34-44 even
Homework #7 Thurs. Oct. 23 Thurs. Oct. 30 5.2: 2, 4, 8, 16

5.3: 8, 12, 14, 16, 20, 24, 26, 30, 36

5.4: 2, 4, 16, 18, 20
Homework #8 Thurs. Oct. 30 Thurs. Nov. 6 5.5: 2, 6, 10, 14, 18, 22, 26, 30, 32, 36, 48, 54

5.6: 2, 4, 6 (graph not required)
Midterm 2 (in class) Thrs. Nov. 13 Midterm2Solutions.pdf
Homework #9 Thurs. Nov. 6 Tues. Nov. 18 Electrical Circuits Problems 4, 8, 12, 18

10.1: 2-10 even, 14, 16, 26-32 even

Computing Portion: HW9Computing.pdf
(helpful file below under Resources)
Homework #10 Tues. Nov. 18 Tues. Nov. 25 10.2: 2-10 even

10.3: 30, 32, 34

10.5: 2, 8, 32, 34 (graphing not required)

7.1: 2, 8

7.2: 4, 8, 12, 14, 24
No Class (Thanksgiving!) Thurs. Nov. 27
Homework #11 Tues. Nov. 25 Thurs. Dec. 4 6.1: 2, 6, 10, 14, 18, 28, 32

7.3: 2*, 6*, 10*, 14*, 28, 30, 36
(* = graphing not required)
#36 Solution
Homework #12 Thurs. Dec. 4 Thurs. Dec. 11 7.5: 2, 6, 10, 14 (graphing not required)

8.1: 2, 4, 6, 10, 20, 22, 24

8.2: 4, 16, 24, 30

10.2: 12, 14
Last day of class Thurs. Dec. 11
Final Exam Take-Home Portion Thurs. Dec. 11 Wed. Dec. 17 TakeHomeFinalSolutions.pdf
Final Exam Wed. Dec. 17 10:30AM-12:30PM, in our classroom

FinalSolutions.pdf

Grading

There will be 12 homework assignments due in class. Check the above schedule for due dates (subject to change, so check back often). Homeworks constitute 30% of the final grade and will include both written and computing assignments.
There will be two midterm exams, each accounting for 20% of the final grade, and a final exam accounting for 30% of the final grade. A small portion of the final exam will be given as take-home problems on the last day of class, to be handed in at the in-class final.

Resources

The math department's tutoring center has tutors available if you want to drop in for extra help in this class. They are located in the T. Benny Rushing Mathematics Center (adjacent to the LCB and JWB). Check their website for the hours when tutors will be there.

Maple Computing Introduction

The following files were used in the Maple Intoduction Sessions run in the first few weeks of the course. You may find them useful:

2250mapleintro.pdf
2250mapleintro.mws (save and open in Maple to read)

The following files will be helpful for Homework 2:

proj1-3.mws - This is a Maple worksheet; save it and load it into Maple. You can see the commands used to perform tasks like the ones you are asked to do in the homework (following what I did in lecture and the example of section 1-3 in the text book). You can hit Enter next to each Maple command to see the result.

proj1-3.pdf - This file has more explanation of the commands used in the Maple worksheet. Scroll down to page 3 under "Using Maple." This file also describes the commands to use in Mathematica and Matlab.

(Note: These were taken from the text book's web page).

The following will be helpful for Homework 3:

HW3Guide.mws - Load this file into Maple. It contains commands for calculations and figures for "1.5 Application: Indoor Temperature Oscillations" from pages 56-58 in the text book.

The following will be helpful for Homework 4:

proj2-4.mws and proj2-4.pdf

The following will be helpful for Homework 9: HW9Guide.mws

<toth[at symbol]math[dot]utah[dot]edu>