**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.

- Section 3.9 page 205: 5, 6, 7, 8.
For 6 and 8:
**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)

- Section 6.1 page 298: 1, 2, 5b, 15, 26 (challenge),
27 (challenge)
**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