Math 306 Problems

Some of the problems will be collected and graded. It is important to do all of the problems to develop your understanding of the material and to help prepare you for the exams.
Each line shows the date and the problems from the text assigned from that date.
There are no problems due April 16th. The fourth lab is due on that date.

Collected Problems

Date     Section Problems
1/13 1.1 1, 3, 5, 6, 7, 9, 11, 12.
1/13 1.2 1, 3, 5, 7, 9, 11, 15, 27, 29, 31, 35, 36, 37.
1/20 1.3 3, 5, 9, 11, 12, 13, 15, 17, 20. (HPGSolver optional).
1/22 1.4 1, 5, 6, 12. Do at least one by hand.
1/22 1.5 1, 3, 7, 9, 12, 15, 17.
1/27 1.6 5, 7, 9, 17, 19, 23, 24, 30, 31.
1/29 1.7 3, 7, 9, 13, 15.
1/29 1.9 1, 3, 4, 9, 12, 15, 24, 26, 27.
2/3 2.1 1, 2, 3, 4, 7, 15, 20, 21.
2/3 2.2 1, 2, 5, 7, 9, 11, 13 (use Maple), 19, 20, 23. (HPGSolver optional)
2/5 2.3 1, 2, 3, 5, 7, 8, 9, 15, 17.
2/5 2.4 1, 2.
2/17 3.1 5, 7, 9, 11 (use Maple), 16, 17, 18, 25, 27, 29, 34, 35.
2/19 3.2 3, 5, 7, 11, 13, 21.
2/24 3.3 3, 5, 9, 13, 19, 21.
2/26 3.4 1, 3, 7, 9, 13, 23.
3/3 3.5 3, 5, 9, 19.
3/5 3.6 1, 7, 9, 11, 15, 23, 38.
3/17 4.1 1, 5, 7, 17, 21, 33.
3/17 4.2 3, 5, 9, 17.
3/19 4.3 3, 5, 9, 11, 15.
3/31 5.1 1, 3, 7, 9, 13, 15.
3/31 5.2 1, 3, 5, 7, 11.
4/2 5.3 1, 2, 3, 9.
4/7 Ch. X 4, 15a, 16a, 18a, 19. In 15, 16, 18, 19, just find the recurrence relation and the first few terms.
4/9 Ch. X 29.
4/9 For the following equations, find the recurrence relation, and compute the first few terms of a series solution:
a) 2y'' + xy' + y = 0.     Soln: the recurrence relation is ak+2=-ak/(2(k+2))
b) y'' + (x-1)y' + y = 0.
c) (1+x2)y'' - y' + y = 0.     Soln: the recurrence relation is ak+2=((k+1)ak+1 - (k(k-1)+1))ak)/((k+2)(k+1))
For the following equations a) Show that x=0 is a regular singular point; b) Find the indicial equation and its roots; c) Find the first few terms for one of the solutions.
d) xy'' + y' - 4y =0;
e) x2y'' + xy' + x2y = 0.
4/14 6.1 3, 9, 10, 15, 19.
4/14 6.2 1, 2, 5, 9, 11, 13, 14.
4/16 6.3 2, 5, 15, 17, 27, 29, 31.