Tufts University
Department of Mathematics
Math 250-03 Homework 1
Due: Thursday, September 20, at 3:00 p.m. (in class).
1. Solve the following ODEs. You may use any method you like, but must show your
Tufts University
Department of Mathematics
Math 250-03 Homework 3
Due: Thursday, October 4, at 3:00 p.m. (in class).
1. (20 points) Find an explicit series solution for
ut = uxx + et sin(3x) 0 < x <
Tufts University
Department of Mathematics
Math 250-03 Homework 4
Due: Thursday, October 11, at 3:00 p.m. (in class).
1. (20 points) Recall the denition of a continuous function: The function f : [a,
Tufts University
Department of Mathematics
Math 250-03 Homework 3
Due: Thursday, October 4, at 3:00 p.m. (in class).
1. (20 points) Find an explicit series solution for
ut = uxx + et sin(3x) 0 < x <
Tufts University
Department of Mathematics
Math 250-03 Homework 2
Due: Thursday, September 27, at 3:00 p.m. (in class).
1. (20 points) Find an explicit series solution for
0 < x < 1, t > 0
ut = Kuxx
Tufts University
Department of Mathematics
Math 250-03 Homework 1
Due: Thursday, September 20, at 3:00 p.m. (in class).
1. Solve the following ODEs. You may use any method you like, but must show your
Tufts University
Department of Mathematics
Math 250-03 Homework 2
Due: Thursday, September 27, at 3:00 p.m. (in class).
1. (20 points) Find an explicit series solution for
0 < x < 1, t > 0
ut = Kuxx
Tufts University
Department of Mathematics
Math 250-03 Homework 4
Due: Thursday, October 11, at 3:00 p.m. (in class).
1. (20 points) Recall the denition of a continuous function: The function f : [a,
Tufts University
Department of Mathematics
Math 250-03 Homework 5
Due: Thursday, November 1, at 3:00 p.m. (in class).
1. (10 points) Let A B C be normed spaces with common norm
dense in B and B is den
Tufts University
Department of Mathematics
Math 250-03 Take-Home Midterm Exam
Due: Thursday, October 25, at 3:00 p.m. (in class). No extensions!
1. (15 points) Let K (x) be a bounded positive function
Tufts University
Department of Mathematics
Math 250-03 Homework 8
Due: Thursday, November 29, at 3:00 p.m. (in class).
1. (15 points) Let (x) be the Dirac delta distribution, and
Denition 1.26. Show t
Tufts University
Department of Mathematics
Math 250-03 Homework 7
Due: Thursday, November 15, at 3:00 p.m. (in class).
1. (10 points) Let H be a Hilbert Space, and A : H H and B : H H be operators wit
Tufts University
Department of Mathematics
Math 250-03 Homework 5
Due: Thursday, November 1, at 3:00 p.m. (in class).
1. (10 points) Let A B C be normed spaces with common norm
dense in B and B is den
Tufts University
Department of Mathematics
Math 250-03 Homework 6
Due: Thursday, November 8, at 3:00 p.m. (in class).
1. (20 points) Prove the following Poincar-Friedrichs Theorem.
e
Dene H1 ([a, b]2
Tufts University
Department of Mathematics
Math 250-03 Homework 6
Due: Thursday, November 8, at 3:00 p.m. (in class).
1. (20 points) Prove the following Poincar-Friedrichs Theorem.
e
Dene H1 ([a, b]2