18.03 Problem Set 2
Due by 12:45 P.M., Friday, February 22, 2008, in the boxes at 2-106, next to the Under-
graduate Mathematics Oﬃce.
I encourage collaboration on homework in this course. However, if you do your homework
in a group, be sure it works to your advantage rather than against you. Good grades for
homework you have not thought through will translate to poor grades on exams.
must turn in your own writeups of all problems, and, if you do collaborate,
you must write on the front of your solution sheet the names of the students
you worked with.
Because the solutions will be available immediately after the problem sets are due,
extensions will be possible
I. First-order diﬀerential equations
W 13 Feb
Solution of linear equations; integrating factors:
EP 1.5, SN
Th 14 Feb
F 15 Feb
Complex numbers, roots of unity: SN 5–6; Notes C.1–3.
T 19 Feb
Complex exponentials; sinusoidal functions: Notes C.4; SN 4; Notes IR.6.
W 20 Feb
Linear system response to exponential and sinusoidal input;
gain, phase lag: SN 4, Notes IR.6.
Th 21 Feb
Complex numbers and exponentials.
F 22 Feb
Autonomous equations; the phase line, stability: EP 1.7, 7.1.
4. (W 15 Feb)
EP 1.5: 1, 2, 5. [Remember to check to see if the equation is separable
5. (F 17 Feb)
Notes 2E-1, 2, 7.
6. (T 21 Feb)
Notes 2E-9, 10. Write each of the following functions
) in the form
). In each case, begin by drawing a right triangle with sides
) + sin(2
). (b) cos(
). (c) cos(
8) + sin(
7. (W 22 Feb)