DORDT COLLEGE MATHEMATICS DEPARTMENT
DIFFERENTIAL EQUATIONS -- MATH 204
(FALL 2006)
PROBLEM SETS Last update:
------------ 12/14/06 3:19 pm
+===============================================================+
|PS|ASSIGNED| DUE |RETURNED| Problems Assigned (In Polking, |
| #| / \ | et al, unless otherwise noted) |
|==+=======+=======+=======+====================================|
|--| 12/13 | ----- | | (Study for final exam, Monday, |
| | | ----- | ----- | 12/18 at 3:30 - 5:30 PM) |
|--+-------+-------+-------+------------------------------------|
|39| 12/11 | 12/13 | | Read 6.1 |
| | | | | Pg. 253 Ex 1, 2 |
| | | 12/13 | 12/14#| |
| | | at | | On Wednesday afternoon, 12/13 there|
| | | 5:00PM| | will be a box near Prof. De Boer's |
| | | | | office door. Drop your homework in|
| | | | | the box by 5 PM for final grading. |
| | | | | |
| | | | | This problem set will be returned |
| | | | | by 5 PM Thursday, 12/14. You will |
| | | | | then be able to pick up your work |
| | | | | from the plastic bin near the |
| | | | | engineering pod door. |
|--+-------+-------+-------+------------------------------------|
|38| 12/08 | 12/11 | | Read 5.7 |
| | | 12/13 | 12/14#| Pg 241 Ex 4, 5 |
| | | | | |
| | | | | Note: Technically in each of |
| | | | | Ex 4 and 5 one should multiply |
| | | | | the given functions by H(t), the |
| | | | | Heavyside function. This is |
| | | | | because the Laplace transform is |
| | | | | one-sided or in other words, the |
| | | | | Laplace transform assumes that f(t)|
| | | | | g(t) etc. are zero for all t < 0. |
| | | | | Thus, where the text states for |
| | | | | example that f(t) = t, one should |
| | | | | actually work with f(t) = t*H(t). |
| | | | | In practice, it makes no difference|
| | | | | to the answers you get, so long as |
| | | | | t > 0. |
| | | | | |
| | | | | This problem set will be returned |
| | | | | by 5 PM Thursday, 12/14. You will |
| | | | | then be able to pick up your work |
| | | | | from the plastic bin near the |
| | | | | engineering pod door. |
|--+-------+-------+-------+------------------------------------|
|37| 12/06 | 12/08 | | Read 5.6 |
| | | 12/11 | 12/13#| Pg. 232 Ex 1, 5, 10, 11 |
|--+-------+-------+-------+------------------------------------|
|36| 12/04 | 12/06 | | Read 5.5 |
| | | 12/08 | 12/11#| Pg. 209 Ex 27 |
| | | | | Pg. 225 Ex 1, 3, 4, 6, 13, 14 |
|--+-------+-------+-------+------------------------------------|
|35| 12/01 | 12/04 | | Read 5.4 |
| | | 12/06 | 12/08#| Pg. 202 Ex 36 |
| | | | | Pg. 214 Ex 1 |
|--+-------+-------+-------+------------------------------------|
|34| 11/29 | 12/01 | | Read 5.3 |
| | | 12/04 | 12/06#| Pg. 202 Ex 20, 35 |
| | | | | Pg. 209 Ex 19 |
|--+-------+-------+-------+------------------------------------|
|33| 11/20 | 11/29 | | Read 5.2 |
| | | 12/01 | 12/04#| Pg. 196 Ex 21, 22, 23, 24 |
| | | | | Pg. 197 Ex 29 |
| | | | | Pg. 201 Ex 1-6 |
|--+-------+-------+-------+------------------------------------|
|32| 11/15 | 11/20 | | Read 5.1 |
| | | 11/29 | 12/01#| Pg. 196 Ex 3, 6 |
| | | | | (Study for test on Friday, 11/17) |
|--+-------+-------+-------+------------------------------------|
|31| 11/13 | 11/15 | | Read 4.5 |
| | | 11/20 | 11/29#| Pg. 177 Ex 3 |
| | | | | Pg. 177 Ex 9 Hint: Trig ID for |
| | | | | sine squared. |
|--+-------+-------+-------+------------------------------------|
|30| 11/10 | 11/13 | | Read 4.3 from heading "Repeated |
| | | 11/15 | 11/20#| Roots" to the end of the section. |
| | | | | Pg. 156 Ex 27, 35 |
|--+-------+-------+-------+------------------------------------|
|29| 11/08 | 11/10 | | Review 4.3 as needed |
| | | 11/13 | 11/15#| Pg. 156 Ex. 11, 17, 18, 25 |
|--+-------+-------+-------+------------------------------------|
|28| 11/06 | 11/08 | | Read 4.3 from heading "Complex |
| | | 11/10 | 11/13#| Roots to heading "Repeated Roots." |
| | | | | |
| | | | | Do probs in Cunningham and Stuller |
| | | | | Ex. 11 parts a and d only, 15, 17 |
| | | | | |
| | | | | Also do problems in Polking et al: |
| | | | | Pg. 156 Ex. 9, 10 |
|--+-------+-------+-------+------------------------------------|
|27| 11/03 | 11/06 | | Read Textbook Appendix, pages |
| | | 11/08 | 11/10#| 595 - 598 and Prof. De Boer's |
| | | | | Lecture Notes on Complex Numbers |
| | | | | |
| | | | | Do probs in Cunningham and Stuller |
| | | | | Ex. 2, 3, 4, 7 parts a and b only. |
| | | | | |
| | | | | Note: For Ex. 4 part b, find the |
| | | | | answers by doing complex arithmetic|
| | | | | and then compare to results of pt a|
|--+-------+-------+-------+------------------------------------|
|26| 11/01 | 11/03 | | Read 4.3 up to "Complex Roots" |
| | | 11/06 | 11/08#| Pg 156 Ex 1, 2, 4 |
|--+-------+-------+-------+------------------------------------|
|25| 10/30 | 11/01 | | Review 4.2 |
| | | 11/03 | 11/06#| Pg 149, Ex 9, 14, 16 |
| | | | | For Ex 9, 14, 16 omit part (i). |
| | | | | PPlane is recommended |
|--+-------+-------+-------+------------------------------------|
|24| 10/27 | 10/30 | | Read 4.2 |
| | | 11/01 | 11/03#| Pg 149, Ex 1-6, 19, 22 |
| | | | | PPlane is recommended for 19 and 22|
|--+-------+-------+-------+------------------------------------|
|23| 10/25 | 10/27 | | Review 4.1 |
| | | 10/30 | 11/01#| Pg 145, Ex 11, 25 |
| | | | | |
| | | | | Note errata on Ex 11 |
| | | | | Note errata on answer to Ex 11 |
|--+-------+-------+-------+------------------------------------|
|22| 10/23 | 10/25 | | Review 4.1 |
| | | 10/27 | 10/30#| Pg 145, Ex 21, 23, 24 |
|--+-------+-------+-------+------------------------------------|
|21| 10/20 | 10/23 | | Read 4.1 from Theorem 1.23 to end |
| | | 10/25 | 10/27#| Pg 145, Ex 9, 10 |
| | | | | Note: Be sure to define variables |
| | | | | and consider units. |
|--+-------+-------+-------+------------------------------------|
|20| 10/18 | 10/20 | | Read 4.1 up to Theorem 1.23 |
| | | 10/23 | 10/25#| Pg 145, Ex 1-8, 13 |
|--+-------+-------+-------+------------------------------------|
|19| 10/16 | 10/18 | | Read 3.3, |
| | | 10/20 | 10/23#| Also see Lecture Notes on Ch 3. |
| | | | | |
| | | | | Pg 126, Ex 7, 8 and for each. . . |
| | | | | a.) Assume continuous compounding |
| | | | | and continuous payments. Solve |
| | | | | using the D.E. model. |
| | | | | b.) Assume monthly compounding |
| | | | | and monthly payments. Solve using |
| | | | | the TVM formula presented in class |
| | | | | and in lecture notes. |
|--+-------+-------+-------+------------------------------------|
|18| 10/13 | 10/16 | | Review 3.1, Read 3.2 |
| | | 10/18 | 10/20#| Pg 116 Ex 16, Pg 120 Ex 2 |
|--+-------+-------+-------+------------------------------------|
|17| 10/11 | 10/13 | | Read 3.1 |
| | | 10/16 | 10/18#| Pg 114 Ex 2, 11, 12 |
| | | | | |
| | | | | In class on Wednesday, 10/11, |
| | | | | students pointed out that Ex 1 on |
| | | | | Pg 114 had been double-posted on |
| | | | | PS #17 and PS #16. This page was |
| | | | | corrected at 3:10 pm on Wed. 10/11.|
|--+-------+-------+-------+------------------------------------|
|16| 10/09 | 10/11 | | Read 2.9 |
| | | 10/13 | 10/16#| Pg 100 Ex 1, 2, 30 |
| | | | | Pg 114 Ex 1 |
|--+-------+-------+-------+------------------------------------|
|15| 10/04 | 10/09 | | Read 2.8 |
| | | 10/11 | 10/13#| |
| | | | | Pg 86 Ex 23, 26 |
| | | | / Pg 91 Ex 1 through 4, 5 through 8 |
| |/---------------------/ |
| | Use the dfield solver (linked from the course web page). |
| | To get full credit your solution must show a dot at each |
| | initial condition (and no other dots that would confuse the|
| | matter). You may set initial conditions and place the dots|
| | by setting initial conditions from the keyboard. In the |
| | "Direction Field" Window, from the top menu click on |
| | "Solution" and then "Keyboard input of initial value." |
| | Alternatively, you may click your mouse on the direction |
| | field plot in order to select an initial condition. If |
| | you do this, be sure to write down the coordinates of the |
| | initial condition (from the lower left corner of the |
| | window) just before you click. After printing, use a |
| | pencil to annotate the plot with the coordinates of the |
| | initial condition(s). The bigger you make the direction |
| | field plot on your computer screen the more accurate you |
| | can be with your mouse cursor. Any reasonably close |
| | results will get full credit. You may put Ex 1 - 4 on one |
| | plot and Ex. 5-8 on another plot. Label each solution with|
| | the Exercise number. |
|--+-------+-------+-------+------------------------------------|
|14| 10/02 | 10/04 | | Read 2.6 to the end, Read 2.7 |
| | | 10/09 | 10/11#| Pg 75 Ex 35, Pg 86 Ex 7, 8 |
| | | | | |
| | | | | On 10/04 errata to the textbook's |
| | | | | answer to Pg 75 Ex 35 was found. |
|--+-------+-------+-------+------------------------------------|
|13| 9/27 | 10/02 | | Review 2.6 |
| | | 10/04 | 10/09#| Pg 75 Ex 12, 14, 33 |
| | | | | (Study for test on Friday, 9/29) |
|--+-------+-------+-------+------------------------------------|
|12| 9/25 | 9/27 | | Read 2.6 thru page 74 |
| | | 10/02 | 10/04#| Pg 75 Ex 9, 11, 27 Note errata |
|--+-------+-------+-------+------------------------------------|
|11| 9/22 | 9/25 | | Review 2.5, Read 2.6 thru page 68 |
| | | 9/27 | 10/02#| Pg 62 Ex 7, Pg 75 Ex 1, 2, 7 |
|--+-------+-------+-------+------------------------------------|
|10| 9/20 | 9/22 | | Read 2.5 |
| | | 9/25 | 9/27#| Pg 61 Ex 1, 2 |
| | | | | See errata on the answer to Ex 1 |
|--+-------+-------+-------+------------------------------------|
| 9| 9/18 | 9/20 | | Review 2.4 |
| | | 9/22 | 9/25#| Pg 55 Ex 23, 37, 38 |
|--+-------+-------+-------+------------------------------------|
| 8| 9/15 | 9/18 | | Review 2.4 |
| | | 9/20 | 9/22#| Pg 55 Ex 7, 10, 22 |
|--+-------+-------+-------+------------------------------------|
| 7| 9/13 | 9/15 | | Review 2.3, Read 2.4 |
| | | 9/18 | 9/20#| Pg 45 Ex 6, 19 |
|--+-------+-------+-------+------------------------------------|
| 6| 9/11 | 9/13 | | Read 2.3 |
| | | 9/15 | 9/18#| Pg 36 Ex 35 |
| | | | | Pg 45 Ex 4 |
|--+-------+-------+-------+------------------------------------|
| 5| 9/11 | 9/11 | | Review Sections 2.1, 2.2 |
| | | 9/13 | 9/15#| Pg 15 Ex 20 Hint: Integrate by |
| | | | | parts twice. |
| | | | | Pg 35 Ex 6 Hint: Factor the right |
| | | | | hand side. |
| | | | | Pg 35 Ex 24 |
| | | | | Pg 35 Ex 23 Note: errata |
| | | | | As mentioned in class on Monday, |
| | | | | 9/11, since due dates were not |
| | | | | posted before class, all students |
| | | | | will get "A" peer grades and the |
| | | | | regular due date will be 9/13. |
|--+-------+-------+-------+------------------------------------|
| 4| 9/06 | 9/08 | | Read 2.2 |
| | | 9/11 | 9/13#| Pg 25 Ex 8 |
| | | | | Pg 35 Ex 1, 4, 13, 18 |
|--+-------+-------+-------+------------------------------------|
| 3| 9/04 | 9/06 | | Read 2.1 |
| | | 9/08 | 9/11#| Do Pg 14 Ex 28, |
| | | | | Pg 25 Ex 2, 3, 4, 10 |
|--+-------+-------+-------+------------------------------------|
| 2| 9/01 | 9/04 | | Read 1.3, |
| | | 9/06 | 9/08#| Do p14, Ex 1, 2, 3, 6, 10 |
|--+-------+-------+-------+------------------------------------|
| 1| 8/30 | 9/01 | | Read Sections 1.1, 1.2 |
| | | 9/04 | 9/06#| On page 6, Do Exercises 1, 4, 7, 10|
| | | | | Hint on #10: The motion is one- |
| | | | | dimensional. When the displacement|
| | | | | is positive the force needs to be |
| | | | | negative and when the displacement |
| | | | | is negative the force needs to be |
| | | | | positive. This is what, "...but |
| | | | | opposite..." means in the problem |
| | | | | statement. See also the errata on |
| | | | | this problem. |
| | | | | |
| | | | | Page 9, Ex. 1, 4, 7, 8, 11, 16 |
+---------------------------------------------------------------+
Note 1) Most odd-numbered exercises have answers in the Appendix
at the back of the textbook.
Note 2) Homework must be ready for peer grading and discussion in
class on the first listed due date. It must be turned in for a
final grade on the second listed due date. Peer grading will be
1/5 (20%) of the homework grade.
Note 3) If a "#" follows the "returned" date, then the solution
key is posted on the cork board across the hall from room S233.
Note 4) Problems sets shown above with no "assigned" date are
tentative. More problems might be added, expected due dates
might change, but problems shown will eventually be assigned.
Note 5) If you are having difficulty reading the latest version of
this page it may have to do with your browser's cached memory.
Read this note on cached pages to solve the problem.