Math 3280:
Differential Equations and Linear Algebra
Spring 2014 Syllabus
Prof. Peckham
- Instructor: Bruce Peckham, Professor, Dept. of Mathematics and Statistics
Office: 140C Solon Campus Center, 726-6188,
bpeckham@d.umn.edu
Office Hours: M 2-3; T -- ; W 2-3; Th 2-3; F 10-11
or by appointment
- Lecture meeting times: MWThF 11:00 - 11:50 (Section 5) or 1:00 - 1:50 (Section 9) in EduE 50
- Graduate Teaching Assistant: Long Chen, 133 SCC, 726-6240. Office Hours: M 3-4, T 2-3, W 3-4.
chen2965@d.umn.edu
- Lab meeting times: Tuesdays 11:00 - 11:50 (Section 6) or 1:00-1:50 (Section 10) in Mon 209 Lab
- Text: Differential Equations and Linear Algebra,
by Edwards and Penny, third edition, Pearson/Prentice Hall, 2010.
- Course Home Page: http://www.d.umn.edu/~bpeckham/3280/S2014/Math3280S2014.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, QUALITATIVE, and NUMERICAL
solutions to differential equations. Anayltical techniques yield a formula for a function which is a solution.
Techniques used include separation
of variables, first order linear techniques, second order constant coefficient
linear techniques (including for nonhomogeneous linear differential equations),
Laplace transforms,
and eigenvalue-eigenvector
techniques for linear two-dimensional systems of first order differential
equations.
Qualitative techniques include sketching solutions using slope fields,
phase lines and phase planes, and verbally describing long term behavior of solutions.
Numerical techniques allow for the approximation of a solution starting from specific initial conditions. The simplest is Euler's method.
Numerical techniques are best implemented using computer software.
Linear algebra topics include the use of matrices in solving systems of linear
algebraic equations, determinants of matrices, vector spaces, and an introduction to
linear transformations, including finding eigenvalues and eigenvectors of
matrices and transformations.
The course material is mostly covered in Chapters 1-10 of the Edwards and Penny
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:
Applied Mathematics: Numerical Methods (Math 3810),
Elementary Real Analysis (Math 4201),
Complex Variables (Math 4230), Operational Methods (Math 4240),
Linear Algebra (Math 4236), Introduction to Abstrac Algebra for Teaching Majors (Math 4370), 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 Useful 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.
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
| ITEM | DATE | TENTATIVE MATERIAL | WEIGHT |
| Test 1 | Thurs. Feb. 13, 6-7:30pm | Ch's 1-2 | 15% |
| Test 2 | Thurs. Mar. 27, 6-7:30pm | Ch's 3,4,5.1-5.3 | 20% |
| Test 3 | Thurs. May 1, 6-7:30pm | Ch's 5-10 | 20% |
| Final | Mon. May 12, 10-11:55pm (SCC 120) | Cumulative | 30% |
| HW,Labs,Quizzes | Weekly | See course web page | 20% |
| Decrease weight of lowest | | | -5% |
| 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.
All assignments and due dates will be posted on the web
at www.d.umn.edu/~bpeckham/3280/S2014/Math3280S2014.html.
Late HW or Labs
Students will be allowed 5 grace days per semester for late homework and 5 days per semester for late labs. Once the grace days are used up, 10% per day will be deducted from any subsequent late assignment/lab until it is one week late. Weekends count as one day.
After that students must make arrangements with the instructor for HW or the TA for labs to hand in work for credit of 50%.
Academic Integrity
This course will adhere to UMD's Student Academic Integrity Policy, which can be found at
www.d.umn.edu/vcaa/StudentAcademicIntegrity.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.
Students with Disabilities
It is the policy and practice of the University of Minnesota Duluth to create inclusive learning environments for all students, including students with disabilities. If there are aspects of this course that result in barriers to your inclusion or your ability to meet course requirements - such as time limited exams, inaccessible web content, or the use of non-captioned videos - please notify the instructor as soon as possible. You are also encouraged to contact the Office of Disability Resources to discuss and arrange reasonable accommodations. Please call 218-726-8217 or visit the DR website at
www.d.umn.edu/access
for more information.
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Tuesday, 21-Jan-2014 17:45:52 CST.