Math256Fall2012

Math 256: Applied Honors Calculus IV: Differential Equations Fall 2012
Lecture Times: Monday, Tuesday, Wednesday and Friday 12:10 - 1:00 p.m.
Lecture Rooms: On MWF, lectures meet in 142 Lorch Hall. On Tuesday, lectures meet in 445 Dennison.
Website: http://www-personal.umich.edu/~alben/UMichMath256Fall2012/index.html

Instructor: Professor Silas Alben
Email: alben at umich.edu (the best way to contact me).
Office: 4855 East Hall, tel. 734-936-1564
Office hours: Weds. 3 - 5 p.m., Fri. 4 p.m. - 5 p.m. (subject to change) or by appointment.

Calendar

Week	Meeting	Date	In Class	Notes
1	Lecture 1	Tues, Sept. 4	s1.1, s 1.2, s 1.3	Read s 1.4
	Lecture 2	W, Sept. 5	s 1.3, s 2.1
	Lecture 3	F, Sept. 7	s 2.2, s 2.3
	HW1 due F, Sept. 14 at 5 p.m. HW is not collected in class; Instead, please scan your HW to a pdf file and email it to 256fall2012@gmail.com. Please show clearly the steps leading to the solution. Write neatly. Please submit solutions to all of the following problems: Checked briefly for completeness only, not correctness: s1.1 #9,19,25,28 (use the matlab code dirfield.m, available from the B&D link below (and used in Lecture 1), to check your answer); s1.2 #5,10; s1.3 #6,11; s2.1 #7,19; s2.2 #4,17 Checked for correctness: s2.1 #29,33 s2.2 #30 (use dirfield.m again here)
2	Lecture 4	M, Sept. 10	s 2.3, s 2.4
	Lecture 5	T, Sept. 11	s 2.4, s 2.5
	Lecture 6	W, Sept. 12	s 2.5
	Lecture 7	F, Sept. 14	s 2.6
	HW2 due F, Sept. 21 at 5 p.m. Checked for completeness: s2.3 #7,10; s2.4 #3,8,32; s2.5 #3,7,19; s2.6 #4,13,27; s2.7 #1. Checked for correctness: s2.3 #6; s2.4 #26; s2.5 #20; s2.6 #29; s2.7 #16 (modify the function eulertest.m to solve this problem).
3	Lecture 8	M, Sept. 17	s 2.7, 3.1
	Lecture 9	T, Sept. 18	s 3.2
	Lecture 10	W, Sept. 19	s 3.3
	Lecture 11	F, Sept. 21	s 3.4
	HW3 due F, Sept. 28 at 8 p.m. Checked for completeness: s3.1 #14,21; s3.2 #9,15,21,26,30; s3.3 #5,11,21,25; s3.4 #6,12,19; s3.5 #8, 15; s3.6 #7, 18. Checked for correctness: s3.2 #39; s3.3 #31; s3.5 #18.
4	Lecture 12	M, Sept. 24	s 3.4
	Lecture 13	T, Sept. 25	s 3.5
	Lecture 14	W, Sept. 26	s 3.6
	Lecture 15	F, Sept. 28	s 3.7
	Upcoming: Exam 1, F, Oct. 5 in class. Covers Lectures 1-13 and corresponding sections of the textbook. The exam will consist of 4-6 questions similar to the HW problems. Suggested study method: Work some problems in each section near the ones assigned for HW.
5	Lecture 16	M, Oct. 1	s 3.8
	Lecture 17	T, Oct. 2	s 4.1
	Lecture 18	W, Oct. 3	Review session
	Exam 1	F, Oct. 5	Exam 1 Solutions
	HW4, due F, Oct. 12 at 8 p.m. Checked for completeness: s3.7 #4,15,19; s3.8 #11,15,19; s4.1 #5,10,16; s4.2 #2,21,32; Checked for correctness: s3.7 #30; s3.8 #14; s4.2 #8.
6	Lecture 19	M, Oct. 8	s 4.2
	Lecture 20	T, Oct. 9	s 4.3
	Lecture 21	W, Oct. 10	s 6.1
	Lecture 22	F, Oct. 12	s 6.2
	HW5, due T, Oct. 23 at 8 p.m. Checked for completeness: s4.3 #3,8,16; s6.1 #6,10,26; s6.2 #15,27,33; s6.3 #11,15,21,25; Checked for correctness: s4.3 #17; s6.1 #16; s6.2 #19; s6.3 #26.
7	Fall Break	M, Oct. 15
	Fall Break	T, Oct. 16
	Lecture 23	W, Oct. 17	s 6.3
	Lecture 24	F, Oct. 19	s 6.4
	HW6, due T, Oct. 30 at 8 p.m. Checked for completeness: s6.3 #36; s6.4 #10,15,17; s6.5 #2,10,16; s6.6 #5,10,16; Checked for correctness: s6.4 #13; s6.5 #9; s6.6 #20.
8	Lecture 25	M, Oct. 22	s 6.5
	Lecture 26	T, Oct. 23	s 6.6
	Lecture 27	W, Oct. 24	s 7.1
	Lecture 28	F, Oct. 26	Lin. Alg. Chap. 1
	HW7, due T, Nov. 6 at 8 p.m. Checked for completeness: s7.1 #6,10,23; Linear Algebra (LA) 1.6 #3abc,7,11; LA2.4 #2,3; LA2.7 #1,2,9,25; Checked for correctness: s7.1 #18; LA1.6 #15; LA2.7 #5.
9	Lecture 29	M, Oct. 29	Lin. Alg. 2.1-2.2+
	Lecture 30	T, Oct. 30	Lin. Alg. 2.5
	Lecture 31	W, Oct. 31	Lin. Alg. 3.2, 3.3
	Lecture 32	F, Nov. 2	Lin. Alg. 3.3, 3.4
	Upcoming: Exam 2, M, Nov. 12 in class. Covers Lectures 14-30 and corresponding sections of the textbooks. The exam will consist of 4-6 questions similar to the HW problems.
10	Lecture 33	M, Nov. 5	Lin. Alg. 6.2
	Lecture 34	T, Nov. 6	Lin. Alg. 6.2
	Lecture 35	W, Nov. 7	Boyce &DiP. s 7.2
	Lecture 36	F, Nov. 9	Review session
	HW8, due T, Nov. 20 at 8 p.m. Checked for completeness: LA 3.6 #1, 3, 9, 13; LA6.3 #2,8; Boyce &DiP. s7.2 #4,8,25; Checked for correctness: LA3.6 #12; LA6.3 #3; Boyce &DiP. s7.2 #23.
11	Exam 2	M, Nov. 12	Exam 2 Solutions
	Lecture 37	T, Nov. 13	s 7.3, 7.4
	Lecture 38	W, Nov. 14	s 7.5
	Lecture 39	F, Nov. 16	s 7.6
	HW9, due Thurs., Nov. 29 at 8 p.m. Checked for completeness: Boyce &DiP. 7.3 #8,9,16,31; 7.4 #4; 7.5 #4,10,16,24; 7.6 #2,10,29; 7.7 #6,12,13; 7.8 #1,8; Checked for correctness: Boyce &DiP. 7.3 #19; 7.4 #6; 7.5 #26; 7.6 #17; 7.7 #7; 7.8 #15.
12	Lecture 40	M, Nov. 19	s 7.7
	Lecture 41	T, Nov. 20	s 7.7
	Lecture 42	W, Nov. 21	s 7.8
	Thanksgiving	F, Nov. 23
	_
13	Lecture 43	M, Nov. 26	s 7.8
	Lecture 44	T, Nov. 27	s 7.9
	Lecture 45	W, Nov. 28	s 8.1
	Lecture 46	F, Nov. 30	s 8.2, 8.3
	HW10, due Fri., Dec. 7 at 8 p.m. Checked for completeness: 7.9 #4,5; 8.1 #6,17; 8.2 #6,8,17; 8.3 #6,8; 9.1 #5,15; 9.2 #7,9,20; Checked for correctness: 7.9 #7; 8.1 #8; 8.2 #8; 9.1 #13.
14	Lecture 47	M, Dec. 3	s 9.1
	Lecture 48	T, Dec. 4	s 9.2
	Lecture 49	W, Dec. 5	s 9.3
	Lecture 50	F, Dec. 7	s
	Additional study problems (not to hand in): 9.3 #3,10; 9.4 #1,8.
15	Lecture 51	M, Dec. 10	s
	Lecture 52	T, Dec. 11	Review session
	Final Exam	F, Dec. 14, 8-10 am.	Location: B844 East Hall (basement).

General Information:

Prerequisites: Math 255 (Note: 256 makes only occasional use of multivariable calculus).
Text: Elementary Differential Equations and Boundary Value Problems (9th edition) by Boyce and DiPrima
Background and Goals: Math 256 is part of the applied honors calculus sequence for engineering and science concentrators. Applications and concepts receive equal treatment. Theorems are stated precisely and are derived, but technical details are omitted. Examples are given to illustrate the theory. Critical thinking and class participation are encouraged. The goal is to provide students with a solid background needed for subsequent courses in mathematics, engineering, or science.
Content: Linear algebra, matrices, systems of differential equations, initial value problems, qualitative theory of dynamical systems (e.g. equilibria, phase space, stability, bifurcations), nonlinear equations, numerical methods. Optional: boundary value problems.

Additional notes:

We will cover a small amount of material on computational methods for differential equations, with some examples and exercises that use MATLAB. You do not need to know any MATLAB at the beginning: you can learn what you need to know during the course.

B&D student companion site with Matlab files, etc.

Matlab tutorial links from J. Rauch.

We will also cover some linear algebra from:
K. Matthews' Linear Algebra Lecture Notes

Please do not use laptops, cell phones, etc. during class except during (hopefully very rare) emergencies. These devices will distract me and others.

Grading:

5%: Clicker questions.
20%: HWs.
20%: Midterm 1, in class, tentative date: Friday, Oct. 5. Please email me immediately if you might not be able to attend on Oct. 5.
20%: Midterm 2, in class, tentative date: Monday, Nov. 12. Please email me immediately if you might not be able to attend on Nov. 12.
35%: Final Exam, Friday, Dec. 14, 8 a.m.- 10 a.m. Location B844 East Hall (basement).

We will have occasional clicker questions during lecture. Your clicker score will be an average of the fraction you answered (i.e. you get some points just for answering) and the fraction you answered correctly. For the first week, the clicker responses won't count towards your grade, to give time to get used to the system. After the first week, you can miss up to eight lectures without losing any clicker points.

As is typical for a course at this level, much of the grade is based on exam performance. A good strategy to do well on exams is to work a wide range of HW problems, possibly beyond those assigned for HW. After a point you become sufficiently familiar with the methods that you can think about them clearly and apply them accurately during the exams.

HWs will be assigned every week or two. You may discuss general ideas for the HW with others, but all your work on the HW should be your own.

All HW to hand in should be scanned to a pdf file and submitted by email to the course email address: 256fall2012@gmail.com. It will be graded and returned via email to the address you sent it from. Please include your last name and the HW number in the subject line. Please save copies of your HW (both the paper and the scanned copy) until after final course grades are submitted in case there are any issues with receiving your HW properly in gmail.

Each HW will consist of a large number of problems graded for completeness, and a small number graded for correctness. The problems graded for correctness will be scored out of 10 points each. Then you'll get a bonus ranging from 0 to 20% (of the total possible "correctness" points) depending on how completely you answered the completeness questions.

Late HW is not accepted. However, the lowest three HW grades will be dropped when computing your average.

The Final, though cumulative, will be weighted towards the final 1/3 of the course.