Date Assigned
|
Date Due
|
Section
|
Page
|
WileyPlus
|
Paper Prob
|
Comments
|
| 16 Jan |
25 Jan |
§1.1 |
7 |
# 12, 13, 15, 17, 19 |
# 4, 5, 15-20 |
For Problems 4 and 5, do not draw the direction field;
instead, draw a direction line (as illustrated in class).
Yes, do both 15, 17, and 19 on WileyPlus and 15-20 on paper.
The practice will be good for you!
Maple worksheet for direction fields
Solutions
|
| 16 Jan |
25 Jan |
§1.3 |
24 |
# 1-6, 15, 16 |
# 9, 12, 14, 28 |
|
| 23 Jan |
28 Jan |
§1.2 |
16 |
# 2, 4a, 7ac |
# 4b, 7b |
Read each question carefully. Be sure you answer the question(s) asked.
For 4b and 7b you can give the answers for the specific equation that
WileyPlus gave you for 4a and 7ac.
See the Direction Field Plotter to help with comparing solutions in 1.
Many of these questions introduce ideas that we will explore in much
greater detail later in the course. Do not worry about trying to do
more than you are asked to do - yet.
Solutions
|
| 23 Jan |
28 Jan |
§2.2 |
48 |
# 1, 4, 9a, 13a, 25 |
# 7, 10ac |
In #24, use the second derivative test to verify that the critical
point is, in fact, a local maximum.
The calculations in #31 should be simpler than the ones we did in class!
Solutions
|
| 25 Jan |
30 Jan |
§2.1 |
39 |
# 4c, 15, 20, 32 |
# 8(c), 16, 31 |
Remember that the standard form for a first-order linear DE
is \( y' + p(t) y = g(t) \).
Solutions
|
| 28 Jan |
4 Sep |
§2.4 |
75 |
# 4, 5, 11, 14 |
# 25 |
|
| 1 Feb |
4 Feb |
§2.6 |
99 |
# 3, 8, 10, 16 |
# 5, 6, 20 |
Remember that the standard form is \( M(x,y)+N(x,y)y'=0 \)
or \( M dx + N dy = 0 \).
Solutions
|
| 8 Feb |
8 Feb |
Exam 1 |
Chapters 1 and 2
(through § 2.6) |
|
| 6 Feb |
15 Feb |
§3.1 |
144 |
# 1, 2, 6, 10, 16, 23 |
# 7, 17, 24 |
The basic form for solutions to linear homogeneous ODEs is \( y=e^{rt} \)
\( \displaystyle \lim_{t\rightarrow\infty} e^{rt} = 0 \) when \( \Re(r)<0 \).
Solutions
|
| 11 Feb |
18 Feb |
§3.2 |
155 |
# 5, 6, 9, 18, 22, 24, 29 |
# 14, 28 |
|
| 13 Feb |
20 Feb |
§3.4 |
172 |
# 2, 3, 8, ,14, 27 |
# 16, 18 |
|
| 15 Feb |
22 Feb |
§3.3 |
164 |
# 9, 11, 19, 36 |
# 23, 31 |
For #31, (13) is Euler's Formula.
For #36, see the text provided with #34.
Solutions
|
| 15 Feb |
27 Feb |
§3.6 |
190 |
# 4, 10, 13, 31 |
# 11, 19 |
For #11 and #19, because the RHS is not given explicitly,
you won't be able to find an explicit formula for the general solution.
Your answers will involve integrals whose integrands will
involve the function g.
Solutions
|
| 22 Feb |
1 Mar |
§3.5 |
184 |
# 1, 2, 5, 11, 16, 20 |
# 12, 21, 25 |
For #21b and #25b you should use Maple, WolframAlpha, or another tool
that will give you the solution to the nonhomogeneous DE. Show this
work (print a screenshot, etc.) and be sure you clearly indicate a
particular solution of the given equation.
Solutions
|
| 25 Feb |
4 Mar |
§4.1 |
226 |
# 1, 4, 8, 10, 24 |
# 17 |
In #1 and #4, if your answer involves more than one interval, enter
your answer in the form \( (a,b) \cup (c,d) \).
Solutions
|
| 27 Feb |
4 Mar |
§4.2 |
233 |
# 3, 11, 19, 31 |
# 8, 38 |
|
| 27 Feb |
5 Mar |
§4.3 |
239 |
# 2, 12, 18 |
# 12 |
Yes! I want you to work #12 twice. Once by hand and once in WileyPlus;
they should be slightly different.
Solutions
|
| 27 Feb |
5 Mar |
§4.4 |
244 |
# 6, 13 |
# 4, 9 |
The two hand-written problems are related; findin the general solution
to the non-homogeneous problem (#4) is needed before you can find the
particular solution satisfying a specific set of initial conditions (#9).
Solutions
|
| 8 Mar |
8 Mar |
Exam 2 |
Chapters 3 and 4
(except §§ 3.7 and 3.8) |
You may bring one notecard (not a full sheet of paper) on which you
have written (i) the factorization of \( 2r^4-r^3-9r^2+4r+4 \)
and (ii) the solution of the linear system
\( \left[\begin{array}{rrrr}
1 & 1 & 1 & 1 \\
1 & 2 &-2 &-\frac{1}{2} \\
1 & 4 & 4 & \frac{1}{4} \\
1 & 8 &-8 &-\frac{1}{8}
\end{array}\right]
\left[\begin{array}{c}
c_1 \\ c_2 \\ c_3 \\ c_4
\end{array}\right]
=
\left[\begin{array}{c}
2 \\ 0 \\ 2 \\ 0
\end{array}\right]
\).
Exam 2
Exam 2 Solution Key
|
| 18 Mar |
25 Mar |
§7.1 |
361 |
#2, 9ab, 10a |
#14 |
For #14, be sure to indicate what happens
if \( a_{12} \) and \( a_{21} \) are both zero.
Solutions
|
| 20 Mar |
25 Mar |
§7.2 |
373 |
# 1a, 2c, 4bc, 10, 14. 21cd |
# 23, 26 |
These should all be review of matrix manipulations.
Solutions
|
| 20 Mar |
25 Mar |
§7.3 |
385 |
# 3, 11, 13, 16, 24 |
(none) |
These should all be review from linear algebra.
|
| 25 Mar |
3 Apr |
§7.4 |
394 |
# 6, 7 |
(none) |
|
| 27 Mar |
3 Apr |
§7.5 |
405 |
# 11, 15 |
# 24-27, 31 |
|
| 29 Mar |
5 Apr |
§7.6 |
417 |
# 1a, 7, 16ab |
# 13, 14 |
Phase Plane Analyzer
is a new tool (in 2013) that I have started to create.
It's written in Maple but you don't have to have a local copy of Maple to
use it. It's still a rough draft. I will make changes as I have time.
Please feel free to make suggestions.
Solutions
|
| 1 Apr |
8 Apr |
§7.8 |
436 |
# 1c, 7a, 9a |
# 1ab, 7b, 11a |
Worked solution to #8.
For #1, use the specific problem you solved in WileyPlus
to answer the questions for (a) and (b).
For #7, use the specific problems you solved in WileyPlus
to answer the question for (b).
For #11, note the special structure of the coefficient matrix.
Solutions
|
| 10 Apr |
15 Apr |
§7.9 |
449 |
# 1, 3, 7 |
# 2, 6 |
For #7 (WileyPlus) see if you can't make a wise guess at the form
of the particular solution.
Solutions
Solution #3
|
| 17 Apr |
17 Apr |
Exam 3 |
Chapter 7 |
|
| 19 Apr |
24 Apr |
§9.1 |
|
# 1b, 4a, 10a, 11ab, 12a, 13, 15 |
# 4b, 10b, 12b |
Phase Plane Analyzer for Linear Systems
is a new tool (in 2013) that I have started to create.
It's written in Maple but you don't have to have a local copy of Maple to
use it. It's still a rough draft. I will make changes as I have time.
Please feel free to make suggestions.
For the problems to be solved on paper, please use the corresponding
problem presented to you by WileyPlus.
In #1b, enter the eigenvector as
a vertical vector with square brackets, e.g.,
\( \left[\begin{matrix} -1 \\ 2 \end{matrix}\right] \).
In #13 and #15, enter the critical point as
a vertical vector with square brackets, e.g.,
\( \left[\begin{matrix} -1 \\ 2 \end{matrix}\right] \).
Solutions
|
| 22 Apr |
24 Apr |
§9.3 |
|
# 5abc, 6a, 10a, 12a, 14abc |
# 6bc, 10bc, 12bc |
Phase Plane Analyzer for Locally Linear Systems
is a new tool (in 2013) that I have started to create.
It's written in Maple but you don't have to have a local copy of Maple to
use it. It's still a rough draft. I will make changes as I have time.
Please feel free to make suggestions.
In #5a and #14a, enter the critical point as
an ordered pair, e.g.,
\( ( -1, 2 ) \).
In #5b and #14b, all you have to enter is the \( 2\times2 \) matrix, e.g.,
\( \left[\begin{matrix} -1 & 2 \\ 3 & -4 \end{matrix}\right] \).
WileyPlus does not have the correct answer in #10a.
For all problems that I've seen, the correct answer should be
\( (0,0) \) and \( (-1,0) \).
In #12, recall that
\( \sin(n\pi)=0 \) and \( \cos(n\pi)=(-1)^n \) for any integer \( n \).
Consider two cases, even and odd, when analyzing the Jacobian.
For the problems to be solved on paper, please use the corresponding
problem presented to you by WileyPlus.
Solutions
|
| 22 Apr |
29 Apr |
§9.4 |
|
# 1bc, 3b, 13bcd |
# 1af, 3acf, 13a |
For #1a and #3a, sketch the nullclines and critical points
instead of the full direction field.
In #13bc, enter the critical points as ordered pairs, e.g.,
\( ( -1, 2 ) \). Note that the answer in #13b will involve the
parameter \( \alpha \).
For the problems to be solved on paper, please use the corresponding
problem presented to you by WileyPlus.
The solutions are being provided in advance of your work to give you
an indication of the type of work I hope to see for the specific version
of the problem that WileyPlus picks for you.
Solutions
|
| 24 Apr |
29 Apr |
§9.5 |
|
# 1f, 3b |
# 1abcde, 3acdef |
For the problems to be solved on paper, please use the corresponding problem presented to you by WileyPlus.
The solutions are being provided in advance of your work to give you
an indication of the type of work I hope to see for the specific version
of the problem that WileyPlus picks for you.
Solutions
|
| 6 May |
6 May |
Final Exam |
Chapters 1, 2, 3, 4,
7, and (some of) 9 |
The exam starts at 12:30pm and concludes 150 minutes later - at 3:00pm.
Grades will be posted as soon as they are completed.
|