﻿ MAT 661 Homework, Fall 2018

# MAT 661 Homework

Due Friday, Sept. 7 (Week 2, Day 2)
Homework 1.

Due Monday, Sept. 17 (Week 4, Day 1)
Homework 2.

Due Monday, Sept. 24 (Week 5, Day 1)
Homework 3.

Due Monday, Oct. 1 (Week 6, Day 1)
Homework 4.
Find two functionally independent first integrals for v = (x, -y, 2z) in two ways:
(1) Find the general solution to the ODE system (1.6), on p. 25. Then eliminate time t in these solutions.
(2) Solve (1.10), on pg. 28.
Book problems:
2.2, 2.6, 2.7(a), 2.8(a)
3.1(a,c), 3.2(a,c)

Due Monday, Oct. 8 (Week 7, Day 1)
Homework 5.
Book problems: 4.1 (a, c, d), 4.2, 5.5(b)
Non-Book Problems:
1. Find the steam function "psi(x,y)" for the vector potential A(x,y,z) = (0, 0, psi(x,y)) that gives the magnetic field of a wire, B = (-y/(x^2 + y^2), x/(x^2 + y^2), 0) on Omega = R^3 take away the z-axis.
2. Fill in the steps of the stream function "psi" for the 2D incompressible Navier Stokes equation, as described here.

Due Monday, Oct. 22 (Week 9, Day 1)
Homework 6.
Book problems from Chapter III: 1.1, 1.2, 2.1(a, c, f, g), 2.2, 2.4

Due Wednesday, Oct. 31 (Week 10, Day 2)
Homework 7.
Book problems from Chapter III: 3.1 (a, c, d, e), 3.4, 4.1, 4.2

Due Wednesday, Nov. 14 (Week 12, Day 2)
Homework 8

Due Wednesday, Dec. 5 (Week 15, Day 2)
Book problems from Chapter V: 1.1, 2.2, 2.3, 3.1, 4.3, 6.1(b), 6.2(b,d), 7.5, 7.5

Note: If this listing is incomplete or disagrees with what I assigned in class, please send me e-mail at Jim.Swift@nau.edu.