# HOMEWORK ASSIGNMENTS

A - Gh Eric D. Andersen
Go - M Yashwan Manick
N - Z Robin E. DeGracia

### Week of March 27 - 31, 2000

#### Assignment 1: Due Wednesday March 29

• Review Chapters 1 - 5 (as necessary)
• Skim Sections 17.1 and 17.5
• Work the problems on the supplementary sheet handed out in lecture. (Not to be handed in!!!) To access the class demo run in lecture on Monday, click here.

• Familiarize yourself with our webpage. Note that all future assignments will be give via this page and not handed out in lecture. Also be sure to check out the Maple info page and/or the comments page.

#### Assignment 2: Due Friday March 31

• Review section 3.4 and read section 17.2. (You can ignore the subsection on homogeneous equations.)
• Work: p. 988: 1, 5, 8, 13, 14, 21.
• Work: p 200: 11, 17, 23.

#### Assignment 3: Due Monday April 3rd

• Review section 7.9 and read section 17.4.
• Do: p. 994: 1, 6, 7, 9, 11 (For 11, solve both as a separable and first order linear differential equation)
• plus the problems below:

1. A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 liters/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank
(a) after t minutes? (b) after 20 minutes?
2. A tank contains 1000 liters of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 liters/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at the rate of 10 liters/min. The solution is kept thoroughly mixed and drains from the tank at 15 liters/min. How much salt is left in the tank
(a)after t minutes? (b)after 1 hour?
3. Into a 2000 liter container is placed 1000 liters of a brine solution containing 40 kg of salt. A brine solution containing .02 kg/l of salt flows into the container at a rate of 50 l/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 25 l/min. How much salt is in the container at the moment it overflows?

### Week of April 3 - 7, 2000

#### Assignment 4: Due Wednesday April 5

• Study: Chapter 6.1
• Do: p. 351: 1, 5, 6, 9, 13, 17, 22, 31

#### Assignment 5: Due Friday April 7

• Study: Chapters 3.7 (skim), 17.1
• Do: pp. 983 - 984: 1, 3, 5, 7, 11, 13, plus the problem below:
• Find the general solution to the differential equation (D-1)(D-2) y = x by solving the system of first order linear differential equations:
1. (D - 2)y = u
2. (D - 1)u = x (solve me first!)

#### Assignment 6: Due Monday April 10

• Read section 17.7 (Ignore Euler equations and complex roots)
• Do: p. 1015: 1, 3, 5, 14, 19, plus the two problems below:

• Find the general solution to the differential equation (D^2 -4)(D -2)y = 0
• Verify that 2x+3 is a solution to the differential equation y'' - 3y' + 2y = 4x, and use this information to find the general solution to this differential equation.

### Note: Our first exam is scheduled for next Wednesday, April 19, from 4:00 - 6:00 pm in 101 Bradley.

#### Assignment 7: Due Wednesday April 12

• Study: Chapters 17.7 (complex roots), Appendix I
• Do: p. 1015: 7, 9, 15, 21 plus the problems below:

1. Write (2 + 3i) / (1 - 5i) in the form a + bi
2. Compute the complex conjugate and modulus of 3 + 4i

#### Assignment 8: Due Friday April 14

• Study: Chapter 7.1
• Do: p. 415: 1, 3, 5, 6, 8

#### Assignment 9: Due Monday April 17

• Study: Chapter 4.8
• Do: p. 287: 1, 3, 5, 7, 9, 11, 13

### Note: Our first exam is scheduled for this Wednesday, April 19, from 4:00 - 6:00 pm in 101 Bradley. See the class homepage for some important information.

#### Assignment 10: Due Wednesday April 19

• Study: The handout that was distributed in class last Friday. If you did not get a copy, the html version of the handout can be found here. The pdf version of the handout can be found here.
• Do: p. 564: 1, 3, 5 (just give the center and radius of convergence, do not worry about the ``interval of convergence''.)
• Also do the following: find the Taylor series for f(x) about the point x = a, and find its radius of convergence for
1. f(x) = 1/(2 x), a = 1
2. f(x) = cos( 4 x ), a = 0

#### Assignment 11: Due Friday April 21

• Study: Sections 9.5, 9.6
• Do: p. 564: 16
• Do: p. 573: 8, 9, 11

#### Assignment 12: Due Monday April 24

• Study: Sections 10.1, 10.2 (through the section "Hanging Chains")
• Do: p. 603: 1, 3, 17, 19
• Do: p. 613: 1, 3(a,b,c), 9

### Week of April 24 - 28, 2000

#### Assignment 13: Due Wednesday April 26

• Study: the rest of Section 10.2
• Do: p. 613: 3(defg), 13, 14, 22

#### Assignment 14: Due Friday April 28

• Study: Section 10.3
• Do: p. 622: 1, 3, 5, 7, 17, 24

#### Assignment 15: Due Monday May 1

• Study: Section 10.4, up to "Lines in 3-Space"
• Do: p. 631: 3, 4, 5, 7, 10

### Note: Our second exam is scheduled for next Wednesday, May 10, from 4:00 - 6:00 pm in 101 Bradley.

#### Assignment 16: Due Wednesday May 3

• Study: the rest of Section 10.4
• Do: p. 631: 15, 16, 17, 21, 25, 27, 28

#### Assignment 17: Due Friday May 5

• Study: The handout distributed on Wednesday. (This handout begins our study of matrices.) If you did not get the handout, you may get the pdf version here. The html version of the handout is here.
• Do: The exercises in the handout.

#### Assignment 18: Due Monday May 8

• Study: The handout distributed on Friday. If you did not get the handout, you may get the pdf version here. The html version of the handout is here.
• Do: The exercises in the handout.

### Note: Our second exam is scheduled for this Wednesday, May 10, from 4:00 - 6:00 pm in 101 Bradley. See the class homepage for some important information.

#### Assignment 19: Due Wednesday May 10

• Study: The handout distributed on Monday. If you did not get the handout, you may get the pdf version here. The html version of the handout is here.
• Do: The exercises in the handout.

#### Assignment 20: Due Friday May 12

• Study: Sections 12.1, 12.2
• Do: p. 701: 1, 3, 5, 12, 14, 19, 20
• Do: p. 706: 1, 3, 5

#### Assignment 21: Due Monday May 15

• Study: Sections 12.3, 12.4
• Do: p. 714: 3, 5, 7, 11
• Do: p. 719: 7, 9, 17, 18

### Week of May 15 - May 19, 2000

#### Assignment 22: Due Wednesday May 17

• Study: Section 12.5 (not including homogeneous functions)
• Do: p. 714: 14
• Do: p. 730: 1, 3, 6, 9, 11

#### Assignment 23: Due Friday May 19

• Study: Sections 12.7 (up to Rates Percieved by a Moving Observer)
• Do: p. 749: 1(ab), 3(ab), 5(ab), 10, 11

#### Assignment 24: Due Monday May 22

• Study: rest of Section 12.7
• Do: p. 749: 1c, 3c, 5c, 7, 9, 14, 17

### Note: Our last class will meet on Tuesday, May 30th, during our x-hour (12:00 - 12:50). There is no class on Monday (May 29th, Memorial Day) or Wednesday (May 31st). Important information concerning the final exam can be found on the class homepage.

#### Assignment 25: Due Wednesday May 24

• Study: Section 13.1 (not including the section on Quadratic Forms)
• Do: p. 778: 1, 3, 5, 7, 9, 11, 17

#### Assignment 26: Due Friday May 26

• Study: Section 13.2
• Do: p. 785: 1, 3, 5, 7, 9

#### Assignment 27: Due Tuesday May 30 (not to turn in)

• Study: Section 13.3
• Do: p. 793: 1, 3, 5, 9, 11
Solutions to this last homework assignment are available in pdf and html formats.