Math 3280 Differential Equations and Linear Algebra Syllabus, Fall 2011

This page will be updated throughout the semester.

Worksheets     Homework     Labs     Resources

Instructor:

Marshall Hampton

Office: 172 SCC

Email: mhampton at d.umn.edu (preferred contact method)

Telephone: 726-6329

Office hours: 1-2 MWThF and 10-11 M, or by appointment.

Class homepage:
http://www.d.umn.edu/~mhampton/m3280f11.html (this page)

Lecture Times:
005: 12:00 P.M. - 12:50 P.M., M,W,F (09/06/2010 - 12/16/2010), EduE 17 and Th in SCC 120.
009: 2:00 P.M. - 2:50 P.M., M,W,Th,F (09/06/2010 - 12/16/2010), EduE 20.

Lab Times:
006: 12:00 P.M. - 12:50 P.M., Tu (09/06/2010 - 12/16/2010), KPlz 143,
010: 2:00 P.M. - 2:50 P.M., Tu (09/06/2010 - 12/16/2010), KPlz 143.

Lab TA:
Xianwu Zhang (zhan2034 at d.umn.edu), office SCC 152.

Prerequisites:
Math 1297 (Calculus II) or equivalent.

Student Conduct Code:
see the full description at www1.umn.edu/regents/policies/academic/Student_Conduct_Code.html.

Textbook:
Differential Equations and Linear Algebra, 2nd or 3rd Edition, Edwards and Penney, Prentice-Hall, is our primary textbook.

Topics:
This course will build on your knowledge of calculus, extending it to differential equations. In addition to their intrinsic mathematical interest, differential equations are applied in a wide variety of fields. In order to understand systems of linear differential equations, we will also learn some basic linear algebra. We will try to cover some sections from every chapter of the book, although more attention will be given to chapters 1 through 7. These will be covered at a pace of roughly one chapter per week.

Exams:
There will be two midterms (tentatively: October 14th and November 18th) and a final exam. A calculator and sheet of notes is allowed on each exam. For the final you can use two pages of notes. Final exam time is not yet determined.

Practice exams:
Practice tests for the midterms and final will be posted here 1 week before the relevant exam.

Practice midterm 1.
Practice midterm 1 solutions.
Practice midterm 2.
Practice midterm 2 solutions.
Practice final.
Practice final solutions.
1st order ODE review worksheet solutions.

Calculator Policy:
Calculators are allowed during exams (note: an internet capable device is not considered a calculator). However, you are expected to show the steps that justify your answers, and to give exact answers whenever possible. This also applies to homework unless the question specifically instructs you to use a computer or calculator. On a test, any step on which you use a calculator must be clearly indicated (just write "CALCULATOR" or "CALC").

Grading:
Grades will be based on your understanding of the material as demonstrated by class participation (mainly worksheets), office hours, homework, labs, and exams. The homework assignments will be weighted equally, with the lowest score dropped. The lowest lab score will also be dropped. Grades will be assigned on a curve. The lowest three worksheet scores will be dropped. The approximate weighting is homework is 15%, each midterm 20%, labs 10%, worksheets 10%, and the final exam is 25%. The final exam may be weighted more versus the midterms if the score is significantly higher.

Worksheets:
Worksheets from class will be posted here.

W 0 Some calculus review.
W 1 Seperable differential equations.
W 2 Slope fields.
W 3 Existence and uniqueness of solutions.
W 4 Linear first order ODEs.
W 5 Linear mixture models.
W 6 Euler's Method.
W 7 Improved Euler and Runge-Kutta methods.
W 8 Homogeneous substitutions.
W 9 Equilibria and stability of autonomous ODEs.
W 10 Air resistance.
W 11 Linear systems of equations.
W 12 Matrix algebra.
W 13 Matrix Inverses.
W 14 Determinants.
W 15 Linear dependence.
W 16 Basis for a solution space.
W 17 Second order constant-coefficient linear ODEs.
W 18 Linear ODEs with constant coefficients.
W 19 Higher-order linear ODEs with constant coefficients.
W 20 Nonhomogeneous linear ODEs with constant coefficients.
W 21 More nonhomogeneous linear ODEs with constant coefficients.
W 22 Nonhomogeneous ODES using variation of parameters.
W 23 Still more nonhomogeneous linear ODEs with constant coefficients
W 24 Eigenvectors and eigenvalues.
W 25 First-order systems
W 26 Review of Chapter 5
W 26 Solutions to worksheet 26.

Homework:
Late homework is not accepted. Your answers should include intermediate steps - it is not acceptable to only write down an answer.

Assignment 1 (due Monday, September 12th).

Assignment 2 (due Monday, September 19th).

Assignment 3 (due Thursday September 29th).

Assignment 4 (due Thursday October 6th).

Assignment 5 (due Thursday October 13th).

Assignment 6 (due Thursday October 27th).

Assignment 7 (due Thursday November 3rd).

Assignment 8 (due Thursday November 10th).

Assignment 9 (due Thursday November 17th).

Assignment 10 (due Friday December 1st).

Assignment 11 (due Thursday December 8th).

Assignment 12 (due Friday December 16th).

Labs:

We will use the computer algebra system Sage for our labs. Sage can be accessed through a browser at either https://rigel.d.umn.edu:8000/ or https://rudolph.d.umn.edu:8000/. You can access that off campus if you are on a VPN connection (see this for how to get on a VPN). If for some reason the server is down, you can also use the worldwide accessible server here although you would have to upload your previous work to it.

Help on Sage: The first two sections of the 'constructions' document (available live from the 'Help' link on a worksheet, or statically here) are especially useful for this course, as are the first few sections of the reference manual. There is also a quick reference sheet that may be helpful. Sage is based on the popular programming language Python; if you want a better understanding of python a good place to start is its official tutorial. A variety of other documentation is available here.

Lab 1 (due 9/21) online published Sage version on rigel server, online published Sage version on rudolph server.

Lab 2 (due 9/27) online published Sage version on rigel server, online published Sage version on rudolph server.

Lab 3 (due 10/4) online published Sage version on rigel server, online published Sage version on rudolph server.

Lab 4 (due 10/18) online published Sage version on rigel server, online published Sage version on rudolph server.

Lab 5 (due 10/25) online published Sage version on rigel server, online published Sage version on rudolph server.

Lab 6 (due 11/8) online published Sage version on rigel server, online published Sage version on rudolph server.

Lab 7 (due 11/22) online published Sage version on rigel server, online published Sage version on rudolph server.

Lab 7 (due 12/13) online published Sage version on rigel server, online published Sage version on rudolph server.


Other materials:

MIT ODE lectures online. This course is somewhat different from ours but there is significant overlap.
Khan Academy. These videos are 15 minutes or less and focus on one topic at a time. Almost all of those in the "Differential Equations" section are relevant to our course.

Policy statement:
The University of Minnesota is committed to the policy that all persons shall have equal access to its programs, facilities, and employment without regard to race, religion, color, sex, national origin, handicap, age, veteran status, or sexual orientation.

Disabilities:
An individual who has a disability, either permanent or temporary, which might affect his/her ability to perform in this class should contact the instructor as soon as possible so that he can adapt methods, materials and/or tests as needed to provide for equitable participation.