Starred problems have solutions in the back of the book. You do not have to turn them in, but you may need to look at them in order to understand the subsequent problems.

Homework # 1: (due September 2)   

Chapter 1, Page 7, #1, 2, 5.
Section 2.2, page 20, #2, 4, 5, 8
For extra credit, do the exploration on page 8.

Homework # 2: (due September 9)
Section 2.1, Page 13, #2, 4, 6, 8, 10.
Section 2.3, Page 23 # 7, 9, 10*
Section 2.4, Page 28 # 4, 8, 12

Homework #3: (due September 16)
Section 3.1, page 42, #6
Exploration on page 43: Steps 1-10 (you can skip 11)
Section 3.2, Page 47: Understand the statement of exercise 4 (you don't have to provide the proof yourself, although it's not a bad idea). Then do #5, 11
Section 3.3, Page 50 #1*, 2, 3, 4, 6

Homework #4 (due September 23)
Section 3.5, Page 56, #4, 5*, 6, 7
Section 4.1, Page 59, #1, 2*, 3, 4*, 6
Section 4.2, Page 61, #2, 3, 5*

Homework #5 (due September 30)
Section 4.3, Page 67, #1, 4, 6*, 9, 10*, 11
Section 4.4   Page 71, #3, 6, 9, 12.
Pages 72-73: Do steps 1-4 of the exploration

Homework #6 (due October 7)
Section 4.5   Page 76, #1, 2, 4, 6, 8
Section 4.6   Page 81, #3, 6, 7, 9, 11
Section 4.8   Page 89, #1*, 3, 5, 8
I also recommend looking at problem 9 on p90, but you don't need to turn it in.

Homework #7 (due October 14)
Section 5.1   Page 102, #2, 4, 8
Exploration after section 5.1, steps 1, 3, 4. Steps 5-8 are also interesting -- give them a look, but don't turn them in.
Section 5.2   Page 107, #2, 3, 4. Feel free to use technology to diagonalize matrices.
Section 5.3   Page 115, #1*, 2, 3, 5

Homework #8 (due October 21)
Section 5.4   Page 119, #1*, 2, 4
Exploration on pages 119-120: Steps 1-3.
Section 5.5   Page 125, #2, 5, 7
Section 5.7   Page 142, #2, 4, 13

Homework #9 (due October 28)
Section 4.9, page 94, #16*, 17*, 18, 19*, 20*
Section 6.1   Page 149, #7, 8
Warning: There is a fairly serious error in the description of W^c in the problems in section 4.9. The definition makes sense, so there actually isn't anything wrong with problem 18 (or any of the other assigned problems), but the use of W^c in problems 10-12 to show that any operator has a Jordan canonical form isn't right. (W^c is not a subspace in general, and it isn't a subspace for the matrix of problems 16-20.)

Homework #10 (due November 4)
Section 6.2   Page 151, #4,5*, 7
Section 6.3   Page 156, # 2, 4, 6*, 7
Section 6.4   Page 161, #1*,2, 3
Section 6.5   Page 166, #7, 8

Homework #11 (due November 11)
Section 6.5, Page 166, # 10, 11. For these problems, you only need to find an ORTHOGONAL basis, not an orthonormal basis. You may find the following identities useful:
$\int$₀^π sin^k(x) dx = 2 if k=1,π/2 if k=2, and 4/3 if k=3.
Section 6.7   Page 175, #3, 4
Exploration after section 6.7 (page 176): all 5 parts.
Section 6.9   Page 186, #1, 4
Exploration after 6.9 (page 188), parts 1 and 5. (The whole exploration is recommended, but only turn in parts 1 and 5.)

Homework #12 (due November 18)
Section 7.1 Page 194, #3, 7. (For 7, try integrating by parts. This space comes up in quantum mechanical treatments of the harmonic oscillator.)
Section 7.2   Page 199, #1, 3, 4
Section 7.3   Page 206, First look at (but don't turn in) problems 3 and 4, whose solutions are in the back of the book. Then work (and turn in) problem 5, which is a generalization of problems 3 and 4. You can leave your answers in terms of the eigenvalues of A. Then study (but don't turn in) problem 6.
Section 7.4   Page 213, #6 (just find the eigenvalues, not the eigenvectors), 10, 13

Homework #13 (due November 25)
Section 7.5   Page 219, #1, 2, 3*
If you are a physics student, you should do the explorations on page 220, which will help explain rotations in quantum mechanics. (No, you're not expected to turn it in.)
Section 8.1   Page 227, #1, 3, 5

Homework #14 (due FRIDAY, December 4)
Section 8.3   Page 235, #1, 5*, 6
Section 8.4   Page 241, #2*, 3, 4. You don't have to compute any Fourier series for problems 3 and 4 -- just look them up from Chapter 6! Also, your sketches don't have to be great -- just a rough picture of what's going on.
Section 8.5   Page 250, #14, 15, 17, 21*, 22