# Homework Assignments for Math 331 Section 3

• Assignment 1   Due Thursday, September 11.
• Section 1.1 page 8:  1, 3, 18
• Section 1.3 page 22:  3, 5, 8, 12, 15, 17, 19, 25
• Section 2.1 page 38:   1, 7, 18 (use integration by parts), 21
• Assignment 2   Due Thursday, September 25.
• Section 2.2 page 45:   10, 21, 24
• Section 2.3 page 57:   8.   You will need to read Example 2 pages 51 to 54 ``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 2.3 page 57:   29.   Hint for 29 part b: Solve the differential equation dx/dt = v(x) where v(x) is your answer in part a.
• Section 2.4 page 72:   14, 21 (Problem 21 is a challenge problem, it will not be graded)
• Assignment 3   Due Thursday, October 2.
• Section 2.6 page 95:  2, 3, 13, 18, 25, 31 (Problem 31 is a challenge problem)
• Section 2.2 page 45:   30
• Assignment 4   Due Tuesday, October 7.
• Section 3.1 page 136:  1, 4, 11
• Assignment 5   Due Thursday, October 16.
• Section 3.2 page 145:   1, 7, 9, 14, 16, 21, 23, 24
• Assignment 6   Due Thursday, October 24.
• Section 3.4 page 158:   2, 3, 11, 17, 18, 39 (a challenge problem. Use problem 34 part a)
• Section 3.5 page 166:   2, 13, 15, 38
• Assignment 7   Postponed to Tuesday, November 4.
• Section 3.5 page 166:   23, 25
• Section 3.6 page 178:  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, November 6.
• Section 3.7 page 183:   1, 3, 5, 10, 13, 23, 29
• Assignment 9   Postponed to Tuesday, November 18.
• Section 3.8 page 197:   5, 8, 10, 17
• Assignment 10   Due Thursday, November 20.
• Section 3.9 page 205:   5, 6, 7, 8. For 6 and 8:
a) Note, that 1 kg = 9.8 Newtons.
b) You will need to read pages 203-205 about forced vibrations with damping.
• Assignment 11   Due Thursday, December 4.
• Section 6.1 page 298:   1, 2, 5b, 15, 26 (challenge), 27 (challenge)
• Section 6.2 page 307: 1, 3, 5, 9, 12, 21, 28 (challenge), 32 (Challenge, use 28)
• Assignment 12   Due Thursday, December 11.
• Section 6.3 page 314: 2, 4, 10, 13, 15, 17, and the challenge problems: 27, 28, 29
• Section 6.4 page 321: 1, 2, 16
• Section 6.5 page 328: 1, 13