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Syllabus for Linear Algebra and Differential Equations

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


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.

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-