Math 3280 Differential Equations and Linear Algebra Syllabus, Fall 2012

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: 11-12:15 MWThF, or by appointment.

Class homepage:
http://www.d.umn.edu/~mhampton/m3280f12.html (this page)

Lecture Times:
003: 10:00 P.M. - 10:50 P.M., M,W,Th,F (09/04/2010 - 12/14/2010), EduE 40.
009: 1:00 P.M. - 1:50 P.M., M,W,Th,F (09/04/2010 - 12/14/2010), EduE 32.

Lab Times:
004: 10:00 P.M. - 10:50 P.M., Tu (09/04/2010 - 12/14/2010), MonH 209,
010: 1:00 P.M. - 1:50 P.M., Tu (09/04/2010 - 12/14/2010), MonH 209.

Lab TA:
Xuran Yan, SCC 152. Office hours to be announced.

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 12th and November 16th) 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 exams will be on December 19th at 12-2 (for section 003) and December 21st at 2-4 (for section 009). An alternate final time will be December 18th, in Engr 290, from 12-2.

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 Exam.
Practice Final Exam 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 20%, each midterm 15%, labs 10%, worksheets 15%, and the final exam is 25%. .

Worksheets:
Worksheets from class will be posted here.

W 0 Some calculus review.
W 1 Separable ODEs.
W 2 Slope fields.
W 3 Existence and uniqueness of solutions.
W 4 Linear 1st order ODEs.
W 5 Modelling with linear ODEs.
W 6 Euler's Method.
W 7 Improved Euler method and the fourth order Runge-Kutta method.
W 8 Homogenous substitutions.
W 9 Autonomous equations, phase plots and equilibria.
W 10 Air resistance.
W 11 Linear systems of equations.
W 12 Matrix algebra.
W 13 Matrix Inverses.
W 14 Determinants.
W 15 Curve-fitting.
W 16 Numerical method review.
W 17 Linear dependence.
W 18 Basis for a subspace of solutions.
W 19 The Wronskian.
W 20 Linear constant-coefficient homogeneous second order differential equations.
W 21 More linear constant-coefficient homogeneous second order differential equations.
W 22 Still more linear constant-coefficient homogeneous second order differential equations.
W 23 Linear constant-coefficient nonhomogeneous second order differential equations.
W 24 More nonhomogeneous linear ODEs with constant coefficients.
W 25 Nonhomogeneous ODEs with constant coefficients; variation of parameters.
W 27 More second order linear nonhomogeneous ODEs with constant coefficients.
W 28 Eigenvectors and eigenvalues.
W 29 Review worksheet.
W 29 solutions Review worksheet solutions.
W 30 Row space, column space, nullspace, range.
W 31 First order systems.
W 32 More first-order systems.
W 33 Euler's method for first-order systems.
W 34 The Laplace transform.
W 35 Initial value problems with the Laplace transform.
W 36 Second order systems.
W 37 Solving systems with the Laplace transform.
W 38 Linearizing a nonlinear system at equilibria.
W 39 Linear compartment modeling: tank problem.
Review of nonhomogeneous 2nd order equations and numerical methods.
Review worksheet solutions

Homework:
Late homework is not accepted without a prior arrangement. Your answers should include intermediate steps - it is not acceptable to only write down an answer.

Assignment 1 (due Friday, September 7th).

Assignment 2 (due Friday, September 14th).

Assignment 3 (due Monday, September 24th).

Assignment 4 (due Friday, September 28th).

Assignment 5 (due Friday, October 5th).

Assignment 6 (due Thursday, October 11th).

Assignment 7 (due Wednesday, October 24th).

Assignment 8 (due Thursday, November 1st).

Assignment 9 (due Friday, November 9th).

Assignment 10 (due Thursday, November 15th).

Assignment 11 (due Friday, November 30th).

Assignment 12 (due Friday, December 7th).

Assignment 13 (ungraded but recommended).

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 9/19) online published Sage version on rigel server, online published Sage version on rudolph server.

Lab 2 (due 9/25) online published Sage version on rigel server, online published Sage version on rudolph server.
Sage notebook file if you want to upload to a different server (such as sagenb.org)

Lab 3 (due 10/5) online published Sage version on rigel server, online published Sage version on rudolph server.
Sage notebook file if you want to upload to a different server (such as sagenb.org)

Lab 4 (due 10/16) online published Sage version on rigel server, online published Sage version on rudolph server.
Sage notebook file if you want to upload to a different server (such as sagenb.org)

Lab 5 (due 10/23) online published Sage version on rigel server, online published Sage version on rudolph server.
Sage notebook file if you want to upload to a different server (such as sagenb.org)

Lab 6 (due 10/30) online published Sage version on rigel server, online published Sage version on rudolph server.
Sage notebook file if you want to upload to a different server (such as sagenb.org)

Lab 7 (due 11/13) online published Sage version on rigel server, online published Sage version on rudolph server.
Sage notebook file if you want to upload to a different server (such as sagenb.org)

Lab 8 (due 11/20) online published Sage version on sage (at UMD) server,
online published Sage version on rigel server,
online published Sage version on rudolph server.
Sage notebook file if you want to upload to a different server (such as sagenb.org)

Lab 9 (due 12/11) online published Sage version on sage (at UMD) server,
online published Sage version on rigel server,
online published Sage version on rudolph server.
Sage notebook file if you want to upload to a different server (such as sagenb.org)


Other resources:

Interactive introduction to Python. This might be easier to use than the CodeAcademy site.
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.
Code Academy's brief intro to Python. Totally optional but recommended.
Udacity course on differential equations. This is a applications and numerical-solution focused course which overlaps our labs a little bit since it uses Python. However, I find the explanations too minimal and I think it would be very challenging to work through this course without a good background in differential equations and some familiarity with Python.

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.