Final exam information:
Thursday, May 5, 9 am-noon
Location for my sections is Gross 107 (for Yuhao's sections, French 2231)
The final exam covers the entire syllabus (through 6.5).
You are not allowed a calculator, notes, or any other resources.
Arrive early and leave plenty of time for breakfast, the bus, etc. Good luck studying!
Math 216D, sections 03-08 - Linear Algebra and Differential Equations
This is the home page for Phil's Math 216 discussion sections. See the course calendar at the bottom of this page for section times and locations, as well as important dates.
Math 216 lectures are taught by Professor Clark Bray; here is the course home page. Course policies and materials (including syllabus, lecture schedule, lecture videos, and past tests) are available there. See also Sakai, which has the lecture notes.
Discussion instructor: Phillip Andreae
Email: pandreae (AT) math.duke.edu
Office: Physics 021 (but office hours will not usually be held here)Thursdays, 4:10 - 5:00 pm, Physics 173
My office hours (as of April 30, these times no longer apply)
Wednesdays, 12:30 - 1:20 pm, Physics 173
Thursdays, 2:30 - 3:20 pm, Physics 047 (between discussion sections 03 and 04)
(All 216 students are welcome to attend the office hours of Prof. Bray, Yuhao Hu, or me.)
Homework
Homework is due every Friday at 4:30 pm sharp, unless announced otherwise. Give it to me in your discussion section or put it in your section's folder outside my office (Physics 021) on Friday afternoon. If you do not see the folders, slide your paper under my office door. Please write your name and section number on the first page, clearly label the textbook sections and problem numbers, and staple all pages together.
Please carefully read Prof. Bray's exams, homework, and grading policies page, including the policies for regrades. Absolutely no late homework will be accepted, except in the case of an excused absence. Turn in excused late assignments the following Friday and remind me then so that I can write a note to the grader.
Assignments will be posted below as they are assigned. See the syllabus and AHP for the problems from each section.
Note that 6.4 and 6.5 homework problems will not be collected, but you should do them on your own.
Exam 3 covers through 6.4.
The final exam covers the entire syllabus (through 6.5).
Notes from discussion section
I will post here any notes that I prepare for discussion section in case they are useful to you. The topics discussed vary between sections each week and I do not usually have time to discuss everything in my notes, so the notes may contain material that was not discussed in your section (which is a good reason to read the notes!).
Week 2, Jan 21-22 - Basics of linear systems and row operations; intro to induction proofs.
Week 3, Jan 28-29 - Existence and uniqueness properties; upper-triangular matrices; transpose; symmetric matrices.
Week 4, Feb 4-5 - Properties equivalent to invertibility; induction examples; multilinearity; det as stretching factor; adjoint.
Week 5, Feb 11-12 - Linear independence; a determinant problem.
Week 6, Feb 18-19 - Span, linear independence, bases; a subspace example.
Week 7, Feb 25-26 - Null/row/column spaces; a DE example.
Week 8, March 3-4 - Homogeneous CCLDE: a challenge problem, 4.2 #24; roots of unity; 3.6 #4 (separable DE, from last week).
Week 9, March 10-11 - Nonhomogeneous CCLDE (undetermined coefficients) and applications examples
Week 11, March 24-25 - Review of #4 from exam 2; linearity (AHP #12-14); bases as "languages"
Week 12, March 31-April 1 - Matrices for linear transformations; changes of basis; eigenvalues/vectors intro
Week 13, April 7-8 - Eigenvalues, similarity, diagonalizability, and Jordan canonical form
Week 14, April 14-15 - No notes. We discussed some problems from past exams relating to inner products, Gram-Schmidt, and orthogonal matrices: from 14-15 spring, exam 3, #1,2,3; from 15-16 fall, exam 3, #1.
Week 15, April 21-22 - Systems of DE's. AHP #17-19. We also discussed some problems from past exams: from 15-16 fall, exam 3, #3-6.
Other resources:
Home page for first-year Duke math courses
Getting help with math, including tutoring
Calendar
I will try to keep the calendar below up to date, but it is not official; Professor Bray will always provide official communication about the course. Also, weekly changes to office hours may not always be reflected on this calendar.