Math 311-NUEN Exercises

Text: Richard E. Williamson and Hale F. Trotter, Multivariable Mathematics, 4th ed., Prentice-Hall, Englewood Cliffs, NJ, 2004.

Section   Exercises
1.1 9, 12, 14, 26, 28
1.2 25, 30, 32
1.3 3, 5, 13, 14, 18, 19
1.4 8, 15, 18, 21
1.5 13, 19, 27
1.6 7, 9, 16
2.1A 5, 9, 12
2.2C 9, 13, 19, 24, 28
2.2D 2, 4, 10, 11
2.3 6, 10, 17, 33, 39
2.4 8, 9, 19, 21, 23
2.5 5, 6, 8, 9, 11, 17, 18
3.1 3, 4, 7, 9, 10, 13, 19, 23, 24
3.2 7-11, 13, 26, 27, 30
3.3 6-8, 11, 15-17, 20, 24, 27
3.4 5-9, 13, 17, 19, 21
3.5B 3, 8, 10, 13, 17, 27, 35, 40, 41
3.5C 1, 3, 4, 11, extra problems 1, 2
3.6A 3, 5, 6, 8, 15, 17
3.6C 2, 3, 8, 11, 13, 16, 19, 21
3.7A 2-5, 7, 8, 11, 13
3.7B 3-5, 7, 8, 11, 12, 17
3.7C 1-3, 5
14.6 3, 7
14.7 2, 5, 7, 8
14.8 3, 5, 9, 22, 23, 31, 32
14.9 2, 5, 7, 13, 15 16
14.10B 3, 5, 9, 15, 16, 23, 30, extra problem 3
14.10C 1, 3, 10
14 Rev. 36

Extra problems

  1. Let A be the matrix given below. Find the dimension of the image of A. Use it and problem 11, § 3.5C to find the dimension of the null space of A.
     1 -2  3  3
     2 -5  7  3
    -1  3  -4  3

  2. Suppose that B is a 7×10 matrix, and that the dimension of the null space of B is 5. What is the dimension of the image (column space) of B?

  3. In polar coordinates r, θ, the diffusion equation has the form,

    ∂u/∂ t = ∂2u/∂r2 + r-1 ∂u/∂r + r-1∂2u/∂θ2.

    Given that u=u(r,t) (no angular dependence), u(a,t) = 0, and assuming that u is continuous at r = 0, separate variables.

Updated 8/30/04 (fjn).