Homework 1 Due: In lecture 1-27

Section 8.1: 16, 20, 22, 28, 30, 36, 40.

Section 8.2: 4, 12, 14, 20.

Section 8.3: 4, 8, 12, 14, 16.

Homework 2 Due: In lecture 2-3

Section 8.4: 5, 6, 7, 8, 10, 12, 14, 18, 22, 24, 26, 28, 30.

Section 8.5: 12, 14, 16, 18, 20, 22, 23, 24, 26, 30, 37, 39.

Section 8.6: 10, 14, 20, 26, 30, 32, 36, 46, 48, 52.

Homework 3 Due: In lecture 2-15

Section 8.8: 6, 10, 12, 18, 19, 20, 23, 26.

Section 8.12: 5, 10, 15, 18, 19, 35, 39, 40.

In addition please turn in a solution to the following problem:

What are the eigenvalues and eigenvectors of a the linear map

given by rotation of 45 degrees about the line

x=t, y=t and z=t in R^3? Explain your answer.

Homework 4 Due: In lecture 2-24

Section 3.1: 2, 4, 5, 9, 14, 16, 18, 20, 26, 28, 31, 34, 36, 39.

Section 3.3: 3, 6, 12, 16, 19, 28, 34, 37, 43, 44, 45, 46, 47, 48, 51.

Homework 5 Due: In lecture 3-3

Section 3.4: 2, 5, 8, 10, 15, 21, 30, 33, 40, 44.

Section 3.6: 3, 6, 9, 16, 17, 27, 32, 39.

Homework 6 Due: In lecture 3-17

Section 3.8: 3, 4, 6, 10, 13, 17, 18, 19 ,20, 21, 27, 29, 33, 34.

Section 9.1: 2, 5, 11, 12, 14, 22, 24, 41, 42.

Section 9.7: 3, 10, 11, 22, 29, 30, 32, 43.

Homework 7 Due: In lecture 3-24

Section 9.8: 17, 20, 21, 27.

Section 9.9: 5, 8, 23.

Section 9.10: 12, 18, 21, 33, 35.

Section 9.11: 27, 32.

Section 9.12: 12, 16, 18, 21, 24.

Homework 8 Due: In lecture 4-5

Section 9.13: 4, 7, 13, 20, 26, 32, 36, 39.

Section 9.14: 3, 6, 11, 16, 18.

Homework 9 Due: In lecture 4-14

Section 9.16: 5, 8, 14, 17, 18.

Section 10.1: 5, 9, 14, 19, 20, 24, 26.

Section 10.2: 3, 7, 14, 22, 30.

Homework 10 Due: In lecture 4-21

Section 10.2: 34, 41, 44.

Section 10.3: 2, 5, 10.

Section 5.1: 1, 3, 6, 9, 11, 12.

In addition, use pplane (http://math.rice.edu/~dfield/dfpp.html) to plot the phase portraits of the following systems.

For each system use the phase portrait to guess the nature of the eigenvalues (distinct, repeated, complex)

and their sign (for complex eigenvalues guess the sign of the real part).

Check your guess using Wolfram alpha (http://www.wolframalpha.com).

1) dx/dt= 5x + y and dy/dt= -2x + 3y

2) dx/dt= 10x - 5y and dy/dt= 8x - 12y

3) dx/dt= 12x - 9y and dy/dt= 4x + 0y

4) dx/dt= -4x + 2y and dy/dt= -(2.5)x + 3y

5) dx/dt= -x + 3y and dy/dt= -3x + 5y

6) dx/dt= 4x - 5y and dy/dt= 5x - 4y

Homework 10 Due: In lecture 4-26 (However, there will be no penalty for late homework turned in to your TA’s mailbox by 4-29)

Section 5.1: 17, 21, 26, 31, 35, 37.

Section 5.2: 5, 9, 16, 19, 25, 27. (For 25 and 27 you only need to find one series solution)