Bruce B. Peckham - Fall 2010 Differential Equations and Linear Algebra

Math 3280: Differential Equations and Linear Algebra

Fall 2010 Syllabus
Prof. Peckham

Instructor: Bruce Peckham, Professor, Dept. of Mathematics and Statistics
Office: 104 Solon Campus Center, 726-6188, bpeckham@d.umn.edu
Office Hours: M 12-1; T -- ; W 1:30-2:30; Th 9:30-10:30; F 9:30-10:30 or by appointment
Lecture meeting times: MWThF 11:00 - 11:50 in EduE 40
Graduate Teaching Assistant: Brett Bozyk, 174 SCC, 726-6251. Office Hours: M 1:30-2:30, T 1-2, Th 1-2. bozyk002@d.umn.edu
Lab meeting times: Tuesdays 11:00 - 11:50 in KPlz 143 Lab
Text: Differential Equations and Linear Algebra, by Edwards and Penny, second or third edition, Pearson/Prentice Hall, 2005/2008.
Course Home Page: http://www.d.umn.edu/~bpeckham/Math3280F2010.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 include separation of variables, first order linear techniques, second order constant coefficient linear techniques (including nonhomogeneous 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. They are best implemented using 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 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: 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 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, 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

ITEM	DATE	TENTATIVE MATERIAL	WEIGHT
Test 1	Fri. Oct. 1 10:55-11:55	Ch's 1-2	15%
Test 2	Thurs. Nov. 4 6-7:30pm	Ch's 3,4,5.1-5.3	20%
Test 3	Thurs. Dec. 9 6-7:30pm	Ch's 5-10	20%
Final	Tues. Dec. 21 10-11:55pm	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/Math3280F2010.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%.

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 218-726-6130 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 Thursday, 23-Sep-2010 15:43:42 CDT.