Math 3280:
Differential Equations with Linear Algebra
Spring 2020 Syllabus
Prof. Peckham
- Instructor: Bruce Peckham, Professor, Dept. of Mathematics and Statistics
Office: 166 Solon Campus Center, 726-6188,
bpeckham@d.umn.edu
Office Hours: MWF 10-11:15,
or by appointment
- Lecture meeting times: MWThF 9:00 - 9:50. MWThF in Cina Hall 308
- Three evening Tests: 5-6:30pm. Mon. Feb. 17, Mon. March 23, Thurs. April 23. Rooms TBA. For each evening test, a regularly scheduled day class will be cancelled.
- Graduate Teaching Assistant: Noah Wong, 133 SCC, 726-7995.
Office Hours: Held in SCC 118 - Undergraduate Computer Lab: Tues. 3-4, Wed. 3-4, Thurs. 1-2
wongx565@d.umn.edu
- Lab meeting times: Tuesdays 9:00-9:50 in Mon 209 Lab.
- Text: Differential Equations and Linear Algebra,
by Edwards, Penny, and Calvis, 4th edition, Pearson/Prentice Hall, 2018.
- Course Home Page: http://www.d.umn.edu/~bpeckham/3280/FS2020/Math3280S2020.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, and viewed graphically.
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, eigenvectors, and nullspaces 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:
Numerical Methods (Math 3810),
Elementary Real Analysis (Math 4201),
Complex Variables (Math 4230), Operational Methods (Math 4240),
Linear Algebra (Math 4236), Introduction to Abstract 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).
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. Also used at UMD for Math 4326.
- 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 | Monday Feb. 17, 5-6:30, Room TBA | Ch's 1-2 | 15% |
| Test 2 | Monday March 23, 5-6:30, Room TBA | Ch's 3,4,5.1-5.3 | 15% |
| Test 3 | Thursday April 23, 5-6:30, Room TBA | Ch's 5-10 (selected sections) | 15% |
| Final | Tues. May 5, 8-9:55am (alternate Fri. May 8, 8-9:55am) Room TBA | Cumulative | 25% |
| Quizzes | 8-10 during semester | See course web page | 8% |
| Assignments | weekly | See course web page | 7% |
| Labs | Tuesdays | See course web page | 15% |
| Total | | | 100% |
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.
Every assignment should include a signed statement indicating
- Outside References Used:,
- I understand all work I am turning in.
The list of outside references should include any people, websites, books, solution manuals, HW sites, ... used - other than the section of the textbook from which the problem came.
If no outside references were used, state NONE, and sign.
Using references without properly acknowledging them is academic dishonesty and will result in a zero for the problem for a first offense, a zero for the full assignment for a second offense,and a zero for the total HW score for the course for a third offense.
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 independently does his/her own writeup.
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, even if it is a first offense.
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 use
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 course homepage
at www.d.umn.edu/~bpeckham/3280/S2020/Math3280S2020.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%.
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 email.
Oversleeping,
poor preparation, slight colds, and cold weather are not valid excuses.
Student Learning Outcomes
By the end of the course, students should be able to
- recognize, define and explain basic differential equations and linear algebra terminology
- determine strategies to determine the solutions to differential equations
- compare and contrast analytical, graphical and numerical solutions to differential equations
- determine stragegies to investigate solutions to linear systems of equations
- apply theoretical linear algebra (vector spaces) to describe solutions to linear homogeneous differential equations
- demonstrate proficiency in using software, numerical techiniques, graphical techniques, and analytic techniques
- demonstrate proficiency in scientific visualization
Broader Course Goals
More broadly, students should develop problem-solving and investigation strategies, and they should develop expertise in numerical techniques, analytical techniques, and scientific vizualization, and
be able to apply these to problems to areas beyond differential equations and linear algebra.
General UMD Policies
UMD recommends policy statements for the following: Student Conduct Code, Instructor and Student Responsibilities, Academic Integrity, Excused Absences, Use of Class Notes and Course Materials, Disability Policy, Sexual Harassment, Equity, Diversity, Equal Opportunity, and Affirmative Action, and Mental Health and Stress Management. Links to full descriptions of these policies are available here. All stated policies apply to this course.
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Friday, 24-Jan-2020 15:06:13 CST.