Homework Assignments for Math 431 Section 6 - Spring 2000

• Assignment 1   Due Thursday, Feb 3.
  • Section 1.1 page 10:  3, 5, 8, 12, 15, 17, 19, 25, 29
  • Section 2.1 page 23:   1, 7, 18 (use integration by parts), 21
• Assignment 2   Due Thursday, Feb 10.
  • Section 2.2 page 30:  *13, *23, 38 (a challenge problem)
• Assignment 3   Due Thursday, Feb 17.
  • Section 2.3 page 38:  *10, *21, *24
  • Section 2.4 page 45:  *10, 17 (Problem 17 is a challenge problem, it will not be graded)
  • 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 2.8 page 88:  *2,*3,*13,*25,31 (Challenge)
• Assignment 4   Due Tuesday, Feb 22.
  • Section 2.9 page 93:  *1, *6, *15a, 15b (Challenge), 21
  • Section 2.10 page 94:  *1, *2, *5, *17, *20, *32
• Assignment 5   Due Thursday, March 9.
  • 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
  • Section 3.2 page 138: 1, 7, *9, *14, 16, *21, 23, *24
• Assignment 6   Due Thursday, March 23.
  • Section 3.4 page 150:   *2, *3, *11, *17, *18, 39 (a challenge problem. Use problem 34 part a)
• Assignment 7   Due Thursday, March 30.
  • Section 3.5 page 159: 2, *13, *15, *23, *25, *38
  • Section 3.6 page 171: 1, 2, *3, *4, *6, *7, 18 (A challenge Problem. Hint: Let L[y]=y''+2y'+5y. You could use the method of undetermined coefficients in a straightforward, though laborious, 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 8   Due Thursday, April 6.
  • Section 3.7 page 177: *1, *3, *5, *10, *13, *23, 29
• Assignment 9   Due Tuesday, April 18.
  • Section 3.8 page 190: 5, 10, *8, *17
• Assignment 10   Due Thursday, April 27.
  • Section 3.9 page 198: *5, *7
  • Section 6.1 page 294: *1, *2, *5b, *15, 26 (challenge), 27 (challenge)
• Assignment 11   Due Thursday, May 4.
  • Section 6.2 page 303: *1, *3, *5, *9, *12, *21, 28 (challenge), 32 (Challenge, use 28)
  • Section 6.3 page 311: *2, 4, *10, *13, *15, *17, and the challenge problems: 27, 28, 29
• Assignment 12   Due Thursday, May 11 (Last class).
  • Section 6.4 page 318: *1, *2, *16
  • Section 6.5 page 324: *1, *13
  • Section 6.6 page 334: (Recommended) 4, 9, 13
  • Section 7.1 page 340: *3, 4, *7, *19
• Assignment 13   Due May 16 (for the review, will not be collected)
  • Section 7.5 page 378: *1, 11, *15, 18