Math 266

Course Policies

Grade calculation: Grades are calculated out of 600 points, made up of 200 points for the final exam, 100 points for each of 2 midterms, 50 points total for the quizzes, and 150 points total for the homework. Final letter grades will be adjusted based on your section's performance on the final: if your section does significantly better than other sections, then all grades will be adjusted up.

WebAssign: The homework is approximately half WebAssign problems. Check the Assignment Sheet to see which problems are assigned each lesson. The WebAssign problems for each week are due next Monday at the beginning of class. You need to have bought and entered an access code within two weeks of joining the class, or you'll be unable to submit your assignments.

The WebAssign problems allow you essentially unlimited chances to enter your answer, except for multiple-choice ones, which give you fewer. If your answer is getting rejected for confusing reasons: make sure you've entered subscripts correctly (you can do this with the little menu at the right), you've closed all open parentheses, and that numerical answers are to at least 4 significant figures.

Hand-Graded Homework: Check the Assignment Sheet to see which problems are assigned each lesson. The homework for each week is due next Monday at the beginning of class; if you can't make it to class, put it in Shraddha Shankar's mailbox on the 8th floor of MATH (under her name). Besides the textbook problems, there are supplementary problems and computer projects. Both can be found on the course website.

Late Homework: Late homework will generally not be accepted. If you ask for an extension before homework is due, though, I will almost certainly give you one.

Quizzes: On most Wednesdays, we will have a 10-minute quiz at the beginning of class, on material from the previous week. The lowest quiz grade will be dropped.

Exams:

Midterm 1: Monday, Sept. 17, ME 1061, 6:30-7:30 PM.
Midterm 2: Monday, Oct. 22, MATH 175, 6:30-7:30 PM.
Final: TBD.

Extra credit: I'll give 10 points of extra credit (i.e. one quiz), added to your total quiz score, if you bring in and present a differential equation, or some other topic related to the class. This can be something that you saw in a different class or in reading a different book, or a model you came up with yourself for some natural or social phenomenon. Your presentation should be around 5 minutes. Just let me know before class, or at the beginning of class, if you want to present. Here are some ideas for presentation topics:

We used a second-order equation with constant coefficients to model a simple RLC circuit. What happens if the circuit gets more complicated -- for example, if some of the components are put in series? Can this also be modelled mathematically?
Find another oscillatory system like a spring or an RLC circuit, and talk about modelling it with a second-order constant-coefficient differential equation.
How does resonance matter to real-world engineering projects, and how do engineers deal with it? You could talk more about bridge collapses, or you could find other examples.
What does it mean for a differential equation to be "stiff"? Can you give examples?
Talk about the Runge-Kutta method, or some other numerical approximation method beyond Euler's method. What method are ode45 and/or dfield using?
Give the general solution to the Euler equation, t²y'' + aty' + by = 0. This will be somewhat parallel to the general solution to the homogeneous equation with constant coefficients: the equation has its own kind of characteristic quadratic, and you see different sorts of solutions depending on whether the roots of this are real and distinct, real and repeated, or complex. This equation is discussed at various points in the exercises to chapter 3.
(Only think about this one if you know some of the math already.) Say something about solving differential equations with power series, and give examples.
If we didn't know about trig, we could define the sine and cosine functions as a certain fundamental set of solutions to the equation y'' = -y. Likewise, the exponential function is a certain solution to the equation y' = y. We've decided that these functions are "elementary", but all this really means is that we give them names and force you to learn about them in precalc; from the perspective of this class, we do this because these differential equations are so simple, and lots of other equations can be transformed to these. Are there other differential equations whose solutions could be added to the bucket of "elementary" functions? Talk about one of them, and tell us about the properties of its solutions.

Links and Resources

I'm fond of the online graphing calculator Desmos.

Wolfram Alpha is capable of handling many hard integrals. You should especially give this a try if you're stuck, or if you're unsure if what you're integrating has an elementary answer. (For example, the integral of e^x/x doesn't have an expression in terms of polynomials, exponentials, trig functions, and so on.) I do expect you to be able to do all of the integration techniques you learned in calculus without using a computer -- they're the basis for many of the more advanced things we're doing in this class. You will be asked about them on exams, and you should integrals by hand on your homework when you can.

Some notes I've written: hyperbolic trig functions; reduction of order; undetermined coefficients for nonhomogeneous linear systems.

Schedule

, and solutions.

Date	Lesson	Notes
08/20	1	We also discussed the dfield program.
8/22	2
8/24	3
8/27	4	Homeworks 1-3 due. Solutions
8/29	5	Quiz 1
8/31	6
9/3	--	No class!
9/5	7	No class Monday 9/3. Homeworks 4-6 due, quiz 2. Solutions
9/7	8
9/10	9	Homeworks 7-8 due. Solutions
9/12	10	Quiz 3
9/14	11
9/17	Midterm review	Midterm at 6:30 PM, ME 1061. Here's a practice midterm.
9/19	12	Homeworks 9-10 due. Solutions
9/21	--	No class!
9/24	13	Homeworks 11-12 due. Solutions
9/26	13-14	Quiz 4
9/28	14
10/1	15	Homeworks 13-14 due. Solutions
10/3	16	Quiz 5
10/5	17
10/8	--	No class!
10/10	Group practice session	Homeworks 15-17 due, Quiz 6. Solutions
10/12	18
10/15	19
10/17	20	Homework 18 due, Quiz 7. Solutions
10/19	21
10/22	Exam review	Midterm at 6:30 in MATH 175. Here is a practice exam, and solutions.
10/24	22
10/26	--	No class!
10/29	23	Homeworks 19-21 and Project 1 due. Solutions
10/31	24	Quiz 8
11/02	25
11/05	26	Homeworks 22-25 due. Solutions
11/07	27	Quiz 9
11/09	28
11/12	28	Homeworks 26-27 and Project 2 due. Solutions
11/14	28-29	Quiz 10
11/16	30
11/19	--	No class!
11/21	--	No class!
11/23	--	No class!
11/26	31	Homework 28-30 due. Solutions
11/28	32	Quiz 11
11/30	33
12/3	34	Homework 31-33 due. Solutions
12/5	35
12/7	Exam review	Homework 34-35 and project 3 due. (Optional!) Solutions

Math 266: Ordinary Differential Equations

Course Information

Course Policies

Links and Resources

Schedule