Math. 412, Sec. 501 (Fulling)

Homework Assignments

Haberman, 4th edition

  1. Wed. Sept. 8: 12.4.4, 12.3.6
  2. Wed. Sept. 15: 2.3.1(b), 2.3.2(d), 2.3.3(a,c), 2.3.6
  3. Wed. Sept. 22: 3.2.2(b,f), 3.3.1, 3.3.3(c), 3.3.14, 3.3.16
  4. Fri. Oct. 1: 2.4.1(a,b), 2.4.2, 2.2.3, 2.5.1(a,d), 2.5.2
  5. Wed. Oct. 6: 7.3.1(d), 7.3.4(b), 7.4.1(b,c), 10.2.2, 10.3.3, 10.3.6
  6. Wed. Oct. 13: 10.3.5, 10.3.13, 10.4.8, 10.4.10 [Solve 10.4.10 by Fourier's method, not d'Alembert's; then show that your solution agrees with d'Alembert's solution by regrouping your formula into left-moving and right-moving terms.], 10.5.16, 10.6.13
  7. Wed. Oct. 20: 9.3.5 [Omit 9.3.5(b); instead, insert 9.3.6(a) and use it to solve 9.3.5(c).], 10.4.3, 10.6.10, and these:
    1. Fill in the details on p. 58 of the class notes:
      1. Show that convolution is commutative: f1 * f2 = f2 * f1.
      2. Prove the convolution formula for the inverse Fourier transform of a product ("Convolution Theorem").
    2. Do the exercise on p. 65 of notes:
      1. Solve the heat equation by separation of variables (or, equivalently, by Fourier-transforming the equation and initial condition).
      2. Express the solution in terms of the Green function H(x-z).
    3. Do the exercise on p. 59 of notes ("check that (*) is correct").
  8. Fri. Oct. 29: Click here.
  9. Wed. Nov. 3: 5.4.1, 5.4.6, 5.5.1(c), 5.5.2, 5.5.8, 5.8.5, 5.8.8(c,d)
  10. Wed. Nov. 10: 5.3.3, 5.3.9, 2.5.3, 2.5.6(a), 2.5.8(c), 7.8.7, 7.8.8 <-- REVISED
  11. Wed. Nov. 17: 7.7.1, 7.7.3, 7.7.8, 7.8.2, 7.9.1(c), 7.9.3(a), 7.5.1, 7.5.2
  12. Mon. Nov. 29: 2.5.4, 5.9.3, 7.8.10
  13. Fri. Dec. 3: 7.10.1(b), 7.10.2(b), 7.10.3(c), 7.10.9(a), 7.10.10(a), 7.10.12 <-- DATE REVISED
    WARNING: HABERMAN USES theta TO MEAN phi AND phi TO MEAN theta!

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Last modified Sat 6 Nov 04