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)