MAT 661 Homework, Fall 2020

Due the night before Monday, Aug. 24 (Week 3, Day 1)
Homework 1.

Due in class (or via email attachment, or in my mailbox in AMB 114), Wednesday, Sept. 9 (Week 5, Day 1, since Monday is Labor Day)
Homework 2.

HW 3: The New Due Date is Wednesday, Sept. 23 (Week 7, Day 2).
Book problems from Chapter 2:
1.1, 1.4, 1.5, 1.7, 1.9
2.2, 2.6, 2.7(a), 2.8(a)

Non-book problem: You may want to do this first. I think it's very straight-forward.
Find two functionally independent first integrals for V = (x, -y, 2z) on the first octant Ω = {(x,y,z) : x > 0, y > 0, z > 0} 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.
For your choice of u₁ and u₂, find the largest set Ω^* containing the first octant on which the functions are functionally independent.

BTW, in Star Trek: The Next Generation, the δ Quadrant is frequently mentioned. In that past I have complained about this, since 3-dimensional space does not have quadrants but rather octants. However, the milky way galaxy is a disk, and I retract my objection:
If we look down on the milky way galaxy from the north (as defined on sol), then we can divide our galaxy into four quadrants. Here is a map I found on the internet.

Due Monday, Oct. 5 (Week 9, Day 1)
Homework 4.
Chapter II, 3.1(a,c), 3.2(a,c)
Chapter II, 4.1 (a, c, d), 4.2,
Optional: Chapter II, 5.5(b)

Exam 1 will be on Wednesday, Oct. 7, during class time. It will cover Homeworks 1 through 4.

Due Monday, Oct. 19 (Week 11, Day 1)
Homework 5.
Book problems from Chapter III: 1.1, 1.2, 2.1(a, c, f, g), 2.2, 2.4

Due Monday, Oct. 26 (Week 12, Day 1)
Homework 6.
Book problems from Chapter III: 3.1 (a, c, d, e), 3.4, 4.1, 4.2

Due Friday, Nov. 6 (Week 13, Day 3)
Homework 7