Differential Equations with Linear Algebra

Spring, 2018

**Syllabus**

- Overview
- Student learning goals
- Expectations
- Homework policies
- How grades are determined
- Academic integrity
- Contacting the professor
- Accomodations for disabilities
- Exceptions

Our main text is “Ordinary Differential Equations and Linear Algebra:
A Systems Approach,” by Todd Kapitula. The focus of this book is
on linear differential equations: scalar equations of *n*^{th}
order, and 1^{st} order systems. We will cover most sections
in Chapters 1-5, perhaps omitting case studies and Section 3.6. Though the
separable ODEs of Section 6.1 are often nonlinear, we will also discuss
how to solve them.

**Student learning goals**.
In this course we learn the fundamentals of linear algebra and
of solving linear ordinary differential equations (ODEs).
Students will be able to

- use terms of linear algebra such as
*linear independence*,*span*,*basis*,*column space*,*dimension*,*subspace*, etc. accurately in their own writing, and understand them correctly when reading assignments and exercises use these terms. - apply Gaussian elimination in diverse settings, such as finding null and column spaces of matrices, finding eigenvectors, inverting a matrix, etc.
- articulate the relationship between solutions of nonhomogeneous linear problems and their homogeneous counterparts, and apply appropriate techniques (factoring the characteristic polynomial, variation of parameters, undetermined coefficients) for finding the homogeneous and particular parts of solutions.
- solve scalar differential equations and initial value problems using analytical techniques such separating variables, and the Laplace transform.
- solve homogeneous systems of ODEs using eigenvalues and eigenvectors.
- derive rudimentary DE models based on physical descriptions of first-order problems.

**My expectations of students**.
As a student in this course, you are expected to

**come to class**each day. Be seated and ready to begin at class start time.**turn off and put away cell phones**.**use electronic devices only to enhance learning**. Ipods, smart phones, tablets, or laptops can be valuable for accessing the textbook or viewing an online homework problem, but are undisciplined use is quite distractive.**come equipped for class**, bringing your textbook (at least have access to it), computing device (likely a graphing calculator), pencil and paper.**read assigned passages**, often (but not always) from the text, and preferably*before*the session in which the material is to be discussed. Remind yourself that reading mathematics is not like reading a novel. You should read to understand every sentence in its given sequence.**submit your work by due dates/times**. WebWork assignments have clearly-marked due times—if ever the WebWork system indicates a different date than the one on the course calendar, contact me to alert me to that fact. But know that the WebWork time is the one in effect; Answers will not be accepted after it is reached. Write-ups of answers to hand-checked problems should be submitted to me at the start of class on the due date. Students submitting these write-ups at the appropriate time should also check their names on the submission list; I will assume responsibility for those (and only those!) submissions. If yours is not among those received, you might place yours in the appropriate folder outside my office in hopes it will be graded, but that is by no means guaranteed.**submit only your own work**. You are encouraged, generally speaking, to consult with other students in order to better understand problems and their solutions. When it comes to the answers you submit, however, the final product must be your own, not a transcription of someone else's responses. The consequences of plagiarizing work will be a zero on the assignment/test of the first instance, and will become markedly more severe if another instance occurs.**participate fully in classroom activities**.**make some effort each day**out of class on activities related to this course. That you should take one day in seven away from all school activities is, nevertheless, highly sanctioned.**take ownership for discerning the relative importance of various concepts**. This is part of what it means to become a good learner. Your professor will indicate sections of material/chapters to be covered on tests, but generally not the specific things within those sections to study.**check your (Calvin) email regularly**, at least once in the evening each day.**take exams at the scheduled times**, contacting me at the earliest possible time if extreme circumstances arise. Cheap airfares, early departures for vacations and the like are not considered valid excuses!**seek help over problems**you are having in the course. Do not set your sights on being able to do homework only. Your goal and mine should be that you are able to speak and write intelligently about the topics we discuss and the questions surrounding them. When you know you are falling short of this goal, be proactive.

**Homework**.
Homework is assigned regularly in this course, with due dates displayed
on the course calendar. Homework assignments come in two varieties:

**WebWork assignments**: These are submitted electronically and graded electronically, as well. For most problems, you may submit answers multiple times. This pairing of “immediate feedback” and having unlimited “do-overs” should be used*cautiously*, It is intended to encourage mastery. But, occasionally, a person's answers devolve into a series of guesses rather than refinements on an initial answer. If you find yourself in such a state, you should set for yourself a limit on submitting guesses.**Hand-checked assignments**: The problems will not be quite as numerous as those you do in WebWork nor, on average, will they be quite as routine, sometimes requiring you to synthesize multiple ideas to find a solution. Each problem offers the opportunity for exercise in writing a mathematical “argument” coherently, from start to finish. So, along with working out a valid solution path, you are expected to present it neatly and clearly, in hardcopy (paper form)—I will not accept electronic versions. Neatness means all of the obvious things, but two things I particularly highlight are that multiple pages should be stapled, and your paper should not have any fringes, as if recently torn from a binder. While you are welcome to discuss these exercises with other students,**your write-up must be your own**.

**Grade Calculations**.
There are various components to your grade. Here is what they are,
along with their relative weights:

- WebWork assignments (9%)
- Hand-checked assignments (8%)
- Exams (3 given during the semester, 19% each, no matter what the number of “points possible” seems to reflect)
- Cumulative final exams (26%)

**Academic integrity**.
Webwork assignments are tailored individually, but vary only in minor
details. You are welcome to work with others as you solve Webwork
problems. While I do not bar you from discussing the hand-checked assignments
with others, I encourage you to attempt these on your own, as they will
better suit their purpose that way. Whether you accept this advice or
not, all write-ups are to be done as if on your own, using your own words.

If an instance of academic dishonesty arises, this will result, in the first instance, in a score of zero for all parties involved. Should there be another instance, this will result in immediate failure of the course.

**Contacting me**.
My office is NH 281. If you are having trouble in the course —
if you do not understand something important or have some special
circumstance that impedes your performance — see me about it
*right away*! **Do not put things off.** The hours
I am intentionally in my office for
meeting with students are posted on my
homepage, as they are subject to change during the semester.
If we cannot connect at one of these times, feel free to
talk with me about an appointed time to meet, or swing
by my office and see if I am available to help.

I may be reached by phone at x66856, but a better way
to reach me for a non-technical question is by email.
If you require my approval for something, do
**not** consider having left a message for me
as equivalent to having obtained that approval.

**Exceptions**.
I reserve the right to make changes or exceptions to course policies —
including those described in this document — either for the entire
class or for specific individuals. The ultimate goal in this course is
**learning**, and formal requirements should not unnecessarily stand in
the way of that. Thus, if you think that any of the conditions of the
course are interfering with learning, please speak with me about this,
and we will see what can be done.

This page maintained by:
Thomas L. Scofield

Department of Mathematics and Statistics,
Calvin College