Math 3280: Differential Equations with Linear Algebra

Fall 2014 Syllabus
Prof. Peckham




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


Grading

ITEMDATETENTATIVE MATERIALWEIGHT
Test 1Friday Oct. 3Ch's 1-215%
Test 2Friday Oct. 31Ch's 3,4,5.1-5.315%
Test 3Friday Dec. 5Ch's 5-10 (selected sections)15%
FinalFri. Dec. 19, 8-9:55amCumulative25%
Quizzes5 during semesterSee course web page10%
AssignmentsweeklySee course web page10%
LabsTuesdaysLabs provided from web page10%
Total100%

General policy statement

Lectures, material in the text, labs, assignments, 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.

Assignments and Ground Rules

Assignments 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 assignments, 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 assignment 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.

Use of technology. My general policy is that technology is appropriate to use to do tasks that you learned to do in earlier courses. Technology is not appropriate to do tasks you are learning for the first time in the course. For example, use of technology for assignments, including calculators and/or Mathematica, for algebraic computations, graphing, and taking derivatives or integrals, is encouraged. You should not use calculators or Mathematica commands which solve differential equations in one step. Whenever you use technology on your assignments you should indicate where it has been used so it is clear to the instructor or grader why intermediate steps are not included in your work. Tests will be made "noncomputational" so that calculators are not needed, but you will be allowed to used them for algebraic tasks and function graphing only. You will be on your honor not to use symbolic capabilities (differentiation, integration, solving differential equations in one step). Explicit restrictions will be stated for each Test.

All assignments and due dates will be posted on the web at www.d.umn.edu/~bpeckham/3280/F2014/Math3280F2014.html.

Late Assignments or Labs

Students will be allowed 5 grace days per semester for late assignments 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 assignments 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 Friday, 05-Sep-2014 20:14:34 CDT.