# Syllabus for Linear Algebra and Differential Equations

**TEXT:** Linear Algebra and differential Equations,
Peterson and Sochacki.

**PREREQUISITE: **Math 236

**COURSE DESCRIPTION: **In this course students will develop an understanding
of the basic

theory, applications and connections of linear algebra and differential
equations. We will cover most

of chapters 1-6 in the text although not necessarily in order. Topic include
vector spaces, matri-

ces, determinants, linear transformations, eigenvectors, first order ordinary
differential equations,

second order linear differential equations and systems of differential
equations. We will use the

software system Maple to explore concepts. Maple is unfortunately NOT a free
program. Maple is

available on the computers in Roop 103 and Burruss 030 and 130.

**GRADING: **The grading will be assigned on a 500 point scale:

A: 450-500

B: 400-449

C: 350-399

D: 300-349

F below 300

There will be no curves and no extra credit. I will assign +/- on an individual
basis. WF's will

not be assigned. Points are assigned as follows:

Quizzes (10) - 100 points

Midterm exams (3) - 100 points each

Project - 2 quizzes

Final exam - 100 points

**QUIZZES:** There will be a 10 point quiz each week that there is not an
exam. This quiz will cover

material through the previous class. Quiz questions will be similar to homework
questions. The 8

best quiz scores will be kept, and the rest will be dropped. There will be no
make up quizzes given

for any reason.

**PROJECT: **A project will be assigned in early November. This will involve
research into an

application of linear algebra or differential equations (or both!) and a poster
presentation during

the last week of class. The project will be worth 20 points and count towards
your quiz grade (this

grade may not be dropped!). More information will be available closer to
November.

**MIDTERMS** **and** **FINAL:** There will be
three midterms during the semester worth 100 points

each and a cummulative final exam worth 100 points. The questions on the exams
will be similar

to homework questions and will contain proofs. If you cannot make it to a
scheduled exam, you

MUST contact the instructor BEFORE the exam if at all possible, or if an
emergency, WITHIN

24 HOURS after the exam if you need to schedule a make up exam. Make up exams
will only be

given for extreme excuses. A doctor's note or some other physical excuse is
required. Dates for

exams (subject to change):

Midterm I - Friday September 18

Midterm II - Friday, October 23

Midterm III - Friday, November 20

Final Exam

- Monday December 7, 10:30am-12:30PM

- Friday December 11, 10:30am-12:30pm

**HOMEWORK:** Homework will be assigned, but not collected. Homework,
however, is of the ut-

most importance! You must keep up with the homework, and do it everyday. We will
have several

days in the schedule devoted to homework problems. However, watching someone do
problems and

understanding them is an entirely different skill than being able to do them
yourself. Be sure that

you have tried the homework problems BEFORE we go over them in class. Here is a
homework

strategy that I recommend:

• Before class, read the section that we will go over.

• That evening, read the section again, paying particular attention to the
example problems.

• Try each homework problem.

• If you can't get started, look for a similar example problem in the
text.

• After getting a solution, check the answer in the back of the book.

• If you are correct, go on.

• If not, put a star by the problem, and try it again.

• If you still cannot solve the problem, even knowing the answer, then put
two stars next to

it, and ask about it in class.

• The next day, try all of the problems with one and 2 stars again. Be
sure that you can do

them without looking at the answer.

• When reviewing for quizzes and exams, pay particular attention to the
starred problems.

**ADDITIONAL HELP:** Expect to put a lot of time and e ort into this class
and homework. Do

NOT allow yourself to fall behind! This class will move quickly, and covers a
broad range of new

topics. If you feel yourself falling behind, come to my office hours to discuss
how to keep up. If you

need extra help, try to find a study group of other students enrolled in 238. Go
to the Science and

Math Learning Center in Room 200 Roop Hall. You are welcome to

e-mail questions to me, but please include the entire question, because I may
not have access to a

book when I answer your e-mail.

**
HONOR CODE** You are to abide by the JMU honor code at all times. Ignorance of
the law is

no excuse. Cheating will not be tolerated and will be prosecuted to the fullest extent.

**Math 245 Spring 2009 VERY tentative outline**

Week 1 **Aug. 24** Class overview, Sections 2.1 (Vector spaces), 2.2
(Subspaces), No class Friday.

Week 2 **Aug. 31** Sections 1.2 (Matrices), 1.1 (Systems of Linear
Equations), Quiz 1 on Monday

Week 3** Sept. 7** Sections 2.2 (Spanning Sets), 1.3 (Inverses of Matrices),
1.5 (Determinants), Quiz

2 on Friday

Week 4 **Sept. 14** Sections 1.6 (Properties of Determinants),** Exam 1**
Friday, Ch.1 and 2.1, 2.2

Week 5 **Sept. 21** Sections 2.3 (Linear Independence and Bases), 2.4
(Dimension, Nullspace, Row

Space, Column Space), 2.5 (Wronskians), Quiz 4 on Friday

Week 6 **Sept. 28** Sections 4.1 (Higher Order Linear differential
Equations), 4.2 (Homogeneous

Constant Coefficient linear DEs), Quiz 5 on Friday

Week 7 **October 5** Sections 4.3 (Method of Undetermined Coefficients), 4.4
(Method of Variation

of Parameters), 4.5 (Applications), Quiz 6 on Friday

Week 8** October 12** Sections 3.1 (First Order DE's), 3.2 (Seperable DE's),
3.4 (Linear DE's), Quiz

7 on Friday

Week 9 **October 19** Sections 3.3 (Exact DE's), 3.6 (Modeling with DE's), **
Exam 2** on Friday,

Chapters 3 and 4

Week 10 **October 26** Sections 5.1 (Linear Transformations), 5.2 (Algebra of
Linear Transforma-

tions), 5.4 (Eigenvalues and Eigenvectors), Quiz 8 on Friday

Week 11** November 2** Sections 5.3 (Matrices of Linear Transformations), 5.5
(Similar Matrices,

Diagonalization), Quiz 9 on Friday

Week 12 **November 9** Sections 6.1 (Theory of Systems of DE's), 6.2
(Homogeneous Systems, Con-

stant Coefficients), Projects assigned, Quiz 10 on Friday

Week 13 **November 16** Section 6.5 Converting DE's to First Order systems,**
Exam 3 **on Friday Ch.

5 and 6.

Week 14 **November 23 **Thanksgiving Break

Week 15 **November 30** Project Presentations, **December 4** Review **
Last Day of Class**

Week 16 **Final Exam: Monday, December 7** 10:30am-12:30pm, **Friday,
December 11** 10:30am-

12:30pm