Homework Assignments for Math 431 Section 2

• Assignment 1   Due Wednesday, September 15.
  • Section 1.1 page 10:  3, 5, 8, 12, 15, 17, 19, 25, 29
• Assignment 2   Due Wednesday, September 22.
  • Section 2.1 page 23:   1, 7, 18 (use integration by parts), 21
  • Section 2.2 page 30:   13, 23, 38
  • Section 2.3 page 38:   10, 21, 24
• Assignment 3   Due Wednesday, September 29.
  • Section 2.4 page 45:   *10, 17 (Problem 17 is a challenge problem, it will not be graded)
  • Section 2.8 page 88:   *13, *25, 31 (Problem 31 is a challenge problem, it will not be graded)
  • Section 2.9 page 93: *6, *15 (part a will be graded, part b is a challenge problem) , 21
  • Section 2.10 page 94: 1, 2, *5, 16 A late hint: use the fact that the integral of du/(a^2+u^2) is (1/a)arctan(u/a) + C. You will need first to complete the square v^2-v+1 = (v-1/2)^2 + 3/4
• Assignment 4   Due Wednesday, October 6.
  • Section 2.10 page 94:   *17, *20, *32
  • Section 2.5 page 55:   *9   (Read Example 2 page 48 ``Compound Interest''. Use the latter half of the example which involves the differential equation
    S' = rS +k
    Note the moral of this problem: start saving early!
  • Section 2.7 page 79:   *15, 16 (Hint for 15 part b: Solve the differential equation dx/dt = v(x) where v(x) is your answer in part a.)
  • Section 3.1 page 128: 1, *4, *11
• Assignment 5   Due Wednesday, October 13.
  • Section 3.2 page 138: 1, 7, *9, *14, 16, *21, 23, *24
• Assignment 6   Due Wednesday, October 20.
  • Section 3.4 page 150: 2, 3, *11, *17, *18, 39 a challenge problem (use 34a).
• Assignment 7   Due Wednesday, October 27.
  • Section 3.5 page 159: 2, *13, *15, *23, 31 (a challenge problem), *38
  • Section 3.6 page 171: *32, *33 (Use the method of 32), more problems from this section will be assigned next week.
  • Section 3.8 page 190: *5, *10
• Assignment 8   Due Friday, November 5.
  • Section 3.8 page 190: *8, *17
  • Section 3.6 page 171: 1, 2, *3, *4, *6, *7, *18 ( Let L[y]=y''+2y'+5y. You could use the method of undetermined coefficients in a straightforward, though laborous, way to find a real valued solution U(t) of
    (*)     L[y]   =   4e^{-t}cos(2t)
    Alternatively, you could look first for a complex valued solution Z(t) for the non-homogeneous equation
    (**)     L[y]   =   4e^{(-1+2i)t}.
    This can be done by the method of undetermined coefficients. Next, write Z(t)=U(t)+iV(t) were U(t), V(t) are real valued functions. Since 4e^{-t}cos(2t) is the real part of 4e^{(-1+2i)t}, then the real part U(t) of Z(t) is a real valued solution of (*). The second method is more sofisticated theoretically, but is much simpler computationally.)
• Assignment 9   Due Friday, November 12.
  • Section 3.9 page 198: *5, *7
  • Section 3.7 page 177: 1, *3, *5, *10, *13, *23, 29
• Assignment 10   Due Monday, November 22
  • Section 6.1 page 294: 1, 2, *5b, *15, 26 (challenge), 27 (challenge)
  • Section 6.2 page 303: *1, *3, *12 (more problems will be assigned from this section)
• Assignment 11   Due Friday, Dec 3
  • Section 6.2 page 303: *5, *9, *21, *28, *32 (use the method of problem 28)
  • Section 6.3 page 311: *2, 4, *10, *13, *15, *17,
    Challenge Problems: 27, 28, 29, 30
• Assignment 12   Due Monday, December 13
  • Section 6.4 page 318: *1, *2, *16
  • Section 6.5 page 324: *1, *13,
  • Section 6.6 page 330: (suggested: 3, 4, 9, 13, 14)
  • Section 7.1 page 340: *3, 4, *7, 18, *19
• Assignment 13   Due Monday, December 20 (will not be graded)
  • Section 7.5 page 378: *1, 11, *15, 18