Math 266 Spring 2007

The official grade distribution for the final is:

A: 176-200
B: 144-168
C: 120-136
D: 104-112
F: 96 and below

The final is currently being graded, and we should have a grade distribution sometime on Friday. If you wish to know your final grade in this course, please email me at that time. Thank you, and have a great summer.

I will be in my office on Monday 4/30/07, from 2pm to 5pm. If you have any questions before the final, please feel free to drop by.

The final will be Tuesday, May 1, 2007, 10:20am-12:20pm, at Loeb Playhouse, and we will be occupying the middle block of the balcony.

I have put together a set of review notes which are available from:

http://www.math.purdue.edu/~mleok/courses/ma266notes.pdf

I strongly suggest taking the practice final exam which is available online:

https://www.math.purdue.edu/academic/files/courses/2007spring/MA266/PRACTICE-PROBLEMS.pdf

The problems on it are quite representative of the kind of problems which will show up on the final.

Additional practice questions are also available at:

http://www.math.purdue.edu/academic/files/courses/2005spring/MA266/fexm03f.pdf

and the solutions to these questions are available at:

http://www.math.purdue.edu/~lspice/2004MA266.html

In the case of real-valued coefficient matrices with complex eigenvalues, the eigenvalues always come in complex-conjugate pairs. Furthermore, given an eigenvalue-eigenvector pair (r, v), (cong(r), cong(v)) is also an eigenvalue-eigenvector pair.

In the 2×2 case, this yields two complex-valued solutions

x1(t)=e^r v
x2(t)=e^cong(r) cong(v)

and x1(t)=cong(x2(t)). So, we can construct real-valued solutions by taking

u(t)=Re(x1(t)) = (x1(t)+x2(t))/2
v(t)=Im(x1(t)) = (x1(t)-x2(t))/(2i)

The real-valued solutions will have the form of an exponential multiplied into a vector involving sines and cosines. The exponent of the exponential tells you whether the solution is spiraling into or away from the origin.

The vector involving sines and cosines indicates whether the spiral is clockwise or counterclockwise. To easily see the sense of the rotation, substitute t=0, and t=pi/(2\mu) into the vector.

The remaining homework assignments 33-35 and Project 3 will be accepted for extra credit, and will be due on Monday, April 30, 2007, by 5pm in front of my office MATH 430.

The following subset of the problems from assignments 33-35 are suggested:

Assignment 33 (7.6): Page 410: 1, 15
Assignment 34 (7.8): Page 428: 3, 8; O
Assignment 35 (7.9): Page 439: 1; P

Assignments 31 and 32 are due on Thursday 4/26/07. We will cover the material for 7.6 and 7.8 on Tuesday and 7.9 on Thursday.

Assignments 29 and 30 are due on Friday 4/20/07.

I will not have office hours on Tuesday 4/17/07, but will extend my office hours on Thursday 4/19/07, from 3pm to 5pm.

The next homework is due on Friday 4/6/07 in the slot in front of my office MATH 430. Please ensure that your homework is placed into the envelope for the correct section.

For the 12pm section, assignments 23, 24, 25 and project 1 are due.

For the 1:30pm section, assignments 24, 25, 26 and project 2 are due.

The second exam for Math 266 will be on Thursday, April 5, in class. It will cover all the material on second order differential equations and higher order differential equations.

It will consist of 8 multiple choice problems, and 4 free response problems.

The final exam for Math 266 will be on Tuesday, May 1, (10:20am-12:20pm), the location is to be decided. There will be a makeup final, if you have a legitimate reason to take this instead, please inform me as soon as possible, and then go to the Calculus Office Math 242 to set up an appointment.