Math 3280 Differential Equations and Linear Algebra
Syllabus
Fall 2002
Prof. Peckham
- Instructor: Bruce Peckham, Assoc. Professor, Dept. of Mathematics and Statistics
Office: 104 Solon Campus Center, 726-6188,
bpeckham@d.umn.edu
Office Hours: M 11-12, T 3:30-4:30, W 2-2:50, Th 2-3, F 12-12:50
or by appointment
- Teaching Assistant: Matt Zagrabelny, 174 SCC, 726-6251. Hours: MW 10-11, Th 2-3
- Meeting times: MWF 1:00 - 1:50 in Chemistry 251
AND Th 10-11 in ABAH 235 (usually odd weeks) OR 10-12 in MonH 209 Mac Lab
(usually even weeks).
- Text: Differential Equations and Linear Algebra,
by Steven W. Goode, second edition, Prentice Hall, 2000.
- Course Home Page: http://www.d.umn.edu/~bpeckham/Math3280F2002.html
- Prerequisites:
One year of Single Variable Calculus (Math 1296 and 1297) or equivalent or
permission of the instructor.
Syllabus
This is an introductory course in Differential Equations and Linear Algebra.
Techniques are developed for obtaining ANALYTICAL, GRAPHICAL, and NUMERICAL
solutions to differential equations. Anayltical techniques include separation
of variables, first order linear techniques, second order constant coefficient
linear techniques (including nonhomogeneous), Laplace transforms,
and eigenvalue-eigenvector
techniques for linear two-dimensional systems of first order differential
equations.
Graphical techniques include sketching solutions using slope fields,
phase lines, and phase planes.
Numerical techniques are mainly used with computer software.
Linear algebra topics include the use of Matrices in solving systems of linear
algebraic equations, determinants, vector spaces, an introduction to
linear transformations, including finding eigenvalues and eigenvectors of
transformations.
The course material is mostly covered in Chapters 1-9 of the Goode text.
The specific sections covered will be announced by the instructor. Some
supplemental material will be occasionally presented in class.
Related material in other courses:
Differential equations relies heavily on Calculus, especially integration.
Linear algebra relies on high school and/or college algebra courses.
Math 3280 is a prerequisite for many Mathematics courses:
Complex Variables (Math 4230), Operational Methods (Math 4240),
Linear Algebra (Math 4236), Numerical Methods (Math 4820),
Optimization and Control (Math 5220), Dynamical Systems (Math 5260),
Modeling with Dynamical Systems (Math 5270), Partial
Differential Equations (Math 5280), Linear Programming (Math 5810),
Numerical Analysis: Approximation and Quadrature (Math 5830),
Numerical Analysis: Systems and Optimization (Math 5840),
and Numerical Differential Equations (Math 5850).
Other References
- Your Calculus textbook
- Differential Equations by Blanchard, Devaney and Hall. Another sophomore
differential equations text. Especially good at emphasizing graphical and
qualitative techniques.
- Fundamentals of Differential Equations, by Nagle and Saff, 4th edition.
Textbook used at UMD before Differential Equations and Linear Algebra were
combined.
- Linear Algebra and its Applications, by David C. Lay. A good alternative
text for linear algebra topics.
- Many other texts at this level exist for both differential equations and
for linear algebra. Any of
them might offer alternative explanations to many topics.
Grading (Topics and dates are tentative)
ITEM: DATE: TENTATIVE TOPICS: WEIGHT:
Exam 1: Thurs. Oct. 3 Ch's 1-2 18%
Exam 2: Thurs. Oct. 31 Ch's 3-5 18%
Exam 3: Thurs. Dec. 5 Ch's 6-8 18%
Final Exam: Tues. Dec. 17 12-2pm Ch 9+cumulative 30%
HW sets, Labs, Quizzes 20%
Drop portion of lowest grade -6%
-------------------------- ---
Total: 100%
General policy statement
Lectures, material in the text, labs, homework sets, and tests are
all intended to complement each other. No one is a replacement for any of the
others. You are, in general, expected to learn material which is covered via
any of these sources.
Homework Sets and Ground Rules
Homework will be turned in roughly every week.
All work should be neatly written,
well-organized, and complete.
See the Department "Minimum Standard Requirements" handout.
For regular homework sets, you are encouraged to exchange
ideas with each other, but each person should write up his/her
solutions completely
in his/her own words. It is never appropriate to give a written version of a
problem to another classmate, except to have the classmate read and
evaluate your work with you present.
It is OK to verbally explain your ideas to another classmate, as long as the
classmate then writes up his/her work on his/her own.
One person copying a classmate’s solutions is expressly forbidden
and will result in both students receiving zeroes for that complete
homework set and facing academic disciplinary action.
It is often instructive to read the problems at the end of
each section and think about how you would solve them, even if you don't actually
attempt to solve them.
Assignments will be confirmed by email, and all past and
current assignments will be posted on the web
at `www.d.umn.edu/~bpeckham/Math3280F2002.html'.
Missed Exams or Quizzes
Missed quizzes or exams will
be assigned a zero score unless you provide a valid written, signed
(by a Doctor, for example) excuse for
your absence; unless it is not possible to do so, you must provide verbal
notice ahead of time to your
instructor for an absence. Arrangements
for a makeup should be made as soon as you know you will miss.
Do not wait for the next
class. You can leave the instructor
a message 24 hours a day by phone or email.
Oversleeping,
poor preparation, slight colds, and cold weather are not valid excuses.
Disabilities
Please inform me of any disabilities of
which I should be aware
in order to provide for equitable participation.
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Wednesday, 04-Sep-2002 14:05:27 CDT.