MATH 204-02 Homework

DORDT COLLEGE MATHEMATICS DEPARTMENT
DIFFERENEIAL EQUATIONS — MATH 204
(FALL 2016)

PROBLEM SETS

(Last update: 12/08/2016 4:11 pm)

PS #	Assigned	Due	Returned	Problems Assigned (In Blanchard et al unless otherwise noted)
38	12/05	12/07	12/08	Topics: Convolution in time = mult. in freq. Read Sec. 6.5 page 609 through 611 only. Also see classroom slides for this day. Do in Sec. 6.5 (p616) +1, +3, 4
37	12/02	12/05	12/07	Topics: Solving DE's with Laplace Transforms Read Sec. 6.4 page 571 through 572 only. Also see classroom slides for this day. Do in Sec. 6.4 (p608) +3, 4, +5, +7
36	11/30	12/02	12/05	Topics: Solving 2nd order DEs with Laplace Read Sec. 6.3 (p587 - 598) Also see classroom slides for this day. Do in Sec. 6.3 (p599 ff) +27, 28, +29, +31, +33
35	11/21	11/30	12/05	Topics: Singularity functions, time-shift, on/off Read Sec. 6.2 (p 578-585) Also see classroom slides for this day. Do in Sec. 6.2 (p585 ff) +1, +3, +5, +9, +11, +15
34	11/18	11/21	11/30	Topics: Solving DE's with Laplace Transforms Read Sec. 6.1 page 571 through 572 only. Also see classroom slides for this day. Also read and consider Problem 27 on page 578 Do in Sec. 6.1 (p577 ff) +19, 20, +21, 24, +25
33	11/14	11/18	11/21	Topics: Inverse Laplace via Partial Fractions Read Sec. 6.1 page 572 through 574 only. Also see classroom slides for this day. Do in Sec. 6.1 (p577) +7, 8, +9, 10, +11, 12, +13, 14
32	11/11	11/14	11/18	Topics: Tables of Laplace pairs and properites Read Sec. 6.1 page 569 through 570 only. Also see classroom slides for this day. Do in this handout 28 through 36
31	11/09	11/11	11/14	Topics: Introduction to the Laplace Transform Read Sec. 6.1 through page 569 only. (p 566-569) Do in Sec. 6.1 (p 577) +1, 2, +3, 4 Hint: You may use a table of integrals.
30	11/07	11/09	11/11	Topics: Sinusoidal Forcing at Resonance Read Sec. 4.3 (p 415-424) Do in Sec. 4.3 (p 424 ff) +1, +5, +9, +11 +21
29	11/04	11/07	11/09	Topics: Sinusoidal Forcing Functions Read Sec. 4.2 (p 403-411) Do in Sec. 4.2 (p 412 ff) +3, +7, +11, +15 part (a) only, +19 Note: The due date was erroneously shown as 11/09 from Friday morning, 11/04 to Saturday morning, 11/05.
28	11/02	11/04	11/07	Topics: Forcing Functions, Particular Solution Read Sec. 4.1 (p 388-399) Do in Sec. 4.1 (p399 ff) +1, 6, +9, +19, +33, +41 Hint: t^me^λt is a type of exponential function, where m is an integer.
27	10/31	11/02	11/04	Topics: Guesswork shortcuts for 2nd order system Read Sec. 3.6 (p 330-342) Do in Sec. 3.6 (p342 ff) +1, +3, +5, +9, +13abc, +15abc Note: For this assignment omit all parts that request a plot or phase portrait. You may check your work with plots, but they will not be graded.
26	10/28	10/31	11/02	Topics: Repeated and Zero Eigenvalues Read Sec. 3.5 (p 315-326) Do in Sec. 3.5 (p327 ff) +1, +3, +7, +11, +19, +21. Note: For this assignment HPGSystemSolver or equievalent software is recommended for making any required plots. These plots will be graded.
25	10/26	10/28	10/31	Topics: Systems Having Complex Eigenvalues Read Sec. 3.4 (p 296-310) Do in Sec. 3.4 (p310 ff) +1, +3, +4, 9, 10, +15. Note: For this assignment you may omit all graphs or sketches you are requested to make. You may use those to check your work, but they will not be graded.
24	10/24	10/26	10/28	Topics: Review Complex Numbers Read Lecture Slides Do each of these problems.
23	10/21	10/24	10/28	Topic: Auton. Lin. Sink, Source, Saddle portraits Read Sec. 3.3 (p 280-293) Do in Sec. 3.3 (p 293 ff) +1, 2, +9, +19, +21, +27bac. Important note: Do all the problems in this assignment without the use of a computer. Instead, use what you know about straight-line solutions, typical saddles, exponentials, etc. Sketch the required graphs by hand. (You may confirm your results using a computer, but such work will not be graded.) Additional note: Problem 27 is easier if you work part (b) first, then do parts (a) and (c). Omit part (d) of Problem 27.
22	10/17	never	never	Topic: Review for test on Wednesday Review Chapter 2 and Chapter 3 through Sec. 3.2 Do in Ch. 2 Review (p224 ff) +1, +3, +5, +7, +9, +13, +17, +19, +21, +31, +33, +35, also in Chapter 3 Review (p376) +1, +3 also study for the test on Wednesday Note: This review assignment will not be turned in for grading. Answers and hints can be found in the back of your textbook.
21	10/14	10/17	10/24	Topics: Eigenvalue, Eigenvector defined. Review Section 3.2 Do in Sec. 3.2 (p277) 4, +11, 16, 20
20	10/12	10/14	10/17	Topic: Straight-line solutions → gen'l sol'n Read Section 3.1, Read Section 3.2 Do in Sec. 3.1 (p 259 ff) +11, +17, 24, +25 also in Sec 3.2 (p 277) do +1, 2
19	10/10	10/12	10/14	Topics: Review SIR model, DE Sys in matrix frm Review Sec. 2.7, Read Sec. 3.1 through p246. Do in Sec. 2.7 (p215) 6, +7, +9 also in Sec. 3.1 (p258 ff) do 6, +9
18	10/05	10/10	10/12	Topic: SIR model of an epidemic Read: Section 2.7 Do in Sec. 2.7 (p 214), +1, 2, +3 Note: PS#17 is also due on Monday, 10/10
17	10/03	10/10	10/12	Note: Project 1 is due on 10/05. Topic: Consequences of Exist. & Uniquness in Syst. Read: Section 2.6 Do in Sec. 2.6 (p208) +1, 2, +3, +5, +8, +10 Note: To turn your Project 1 assignment in, Navigate to your grades for MATH 204 in Canvas. Find "PJ#1" and click on it. A "Submission Details" window will open. Look for the "Submit Assignment" link. Click it and follow on-screen instructions from there.
16	9/30	10/03	10/10	Topics: Decoupled, partially decoupled systems Characteristic equation Read Section 2.4, class notes Do in Sec. 2.4 (p194) +1, 4, +7, +11, +13.
15	9/28	9/30	10/05	Topic: Intro to Harmonic Oscillations Read Section 2.3 Do in Sec. 2.3 (p 187) +1, 2, +3, 5, 7a, 8abc
14	9/26	9/28	9/30	Topic: Vector Fields Read Section 2.2 Do in Sec. 2.2 (p 178 ff) 16a, 18ab, +19bcd, +21, +23 For problems 16, 18 and 19 please turn in only the listed parts for grading. Please think about each entire problem however. Remember that on tests you will not have the use of a computer.
13	9/21	9/26	9/28	Study for test on Friday, 9/23. Topic for Wed. Class: Matrices and Vectors Read Section 2.2 Do in Sec. 2.2 (p 178 ff) 2abe, 6abe, +7ac For problems 2, 6, and 7 please turn in only the listed parts for grading. Please think about each entire problem however. Remember that on tests you will not have the use of a computer. This problem set is due for grading on Monday.
12	9/19	9/21	9/26	Topics: Introduction to modeling of systems. Read Section 2.1 Do in Sec. 2.1 (p 161 ff) +1, 2, +3, 4, +5, 6, +7, 16, +19 Note: In every case where you are asked to "confirm your answer using. . ." your confirmation will not be graded and you do not need to write anything down about it. You should still do it to be sure your previous work on the problem is correct.
—	9/16	10/05	12/01 via e-mail and Canvas	Project #1 Read (page 147-148 in your textbook) "Lab 1.5, Modeling Oil Production." (You are NOT required) to do the lab—just read it.) Read "Is there a Christian View of Everything..." by Roy Clouser. Read the entire book of Jonah (in the Bible). As you read, imagine you are Jonah. Pay attention to what Jonah thought the future held and how that made him feel emotionally. Write: A 500 to 2000 word essay to answer the question: "Can differential equations be used to predict future events?" Your essay may optionally refer to additional sources. Your essay must conform to either APA or ASME or IEEE style guidelines. (The entire paper must be on one style.) The abstract must be 150 words or less. (The abstract does not count toward the 500 word minimum or the 2000 maximum.) Grading Rubric: The grade will be a weighted average of three items: Style, Content, and Accuracy The item on which you get the lowest grade will be given 50% weight. The others 25% There is one exception: If you get an "F" for accuracy the whole paper will get an "F." Style: A = Conforms to one of APA, IEEE, etc. styles and has fewer than two grammar and/or spelling problems per page. C = A vestige of APA, IEEE, etc style is there. There are about four grammar and/or spelling errors per page Content: A = Exactly one thesis statement is easy to find in the paper. The thesis is on-topic. The paper is organized to support the thesis. B = A single thesis is present but the paper does not address potential aspects of the thesis that should be defended. C= Several unique thesis statements seem to be present. The paper lacks focus on a single thesis. Accuracy: A = All claims made have supporting references. All conclusions derived from claims make logical sense. C = Some claims have no support, or some derived claims are not clearly logical. F = Fabricated references or other dishonesty. Note: To turn your Project 1 assignment in, Navigate to your grades for MATH 204 in Canvas. Find "PJ#1" and click on it. A "Submission Details" window will open. Look for the "Submit Assignment" link. Click it and follow on-screen instructions from there.
11	9/16	9/19	9/22	Topics: Review Chapter 1 and Project Intro. Reading: Review Chapter 1 Do in "Review Exercises for Chapter 1" (p 136 ff) 2, 10, 12, 14, 18, 20, 30, 34, 38, 54
10	9/14	9/16	9/19	Topics: Integrating factors for linear D.E. Read: Sec. 1.9 Do in Sec. 1.9 (p 133 ff) +1, +3, 4, +9, 10, +11, +13 +23 +24
9	9/12	9/14	9/16	Topics: def'n of Linear D.E. vs. Linearity Read Sec. 1.8 Do in Sec. 1.8 (p 121 ff) +1, 2, +3, +9, 10, +11, +13, +15, +17, 20, +23
8	9/09	9/12	9/14	Topics: Bifurcations Read Section 1.7 Do in Sec. 1.7 (p106) +1, 2, +3, +7, +11, +13, 18, 19ab (skip part c)
7	9/07	9/09	9/12	Topics: Stable/unstable equilibria, phase line Read Section 1.6 Do in Sec. 1.6 (p 89 ff) +1, +5, 8, +13, 20, 30, +31, +37
6	9/05	9/07	9/09	Topics: Existence and Uniqueness of Solutions Read Sec. 1.5 Do in Sec. 1.5 (p72) +5, 6, +7, 8, +9, +11 Optional: Fractal Zoom video
5	9/02	9/05	9/07	Topics: Review modeling, Euler's method Review Sec. 1.3, Read Sec. 1.4 Do in Sec. 1.3 (p 50) +17, 18. Do in Sec. 1.4 (p 61) +3, +5, +15 For Part (a) of problems in Sec. 1.3 plot what can be plotted of the slope field. Use of a computer to make these plots is optional. Use a computer for problems in Sec. 1.4
4	8/31	9/02	9/07	Topics: Direction Fields Read Sec. 1.3 Do in Sec. 1.3 (p47 ff) +1, 6, +7, 10, 12, +15. For problems +7 and 10 skip part (a)*. Add part (c) Solve the D.E. using separation of variables. Use the solution of the D.E. to very accurately calculate and plot at least three points of the solution on the slope-field curve of part (b). Plotting the initial condition does not count as one of the three requested points. Hopefully that's obvious. Note: You may use the textbook's recommended program, DE Tools, or another called dfield. To print plots, do a screen capture (alt-PrintScreen) and paste the result into a word processor document, then print that document.
3	8/29	8/31	9/02	Topics: Review initial value sol'n of a D.E. Modeling real-world situations Review Sec. 1.2. Do in Sec. 1.2 (p34 ff) +29, 30, +33, +39, +41.
2	8/26	8/29	8/31	Topics: What is a solution to a DE? A fundamental technique: Separation of Variables Review Sec. 1.1, Read Sec. 1.2 Do in Sec. 1.1 (p14 ff) 20, Do in Sec. 1.2 (p33 ff) +1, 4, 8, +9, 10.
1	8/24	8/26	8/29 See notes 6 and 9 below	Topics: What are Differential Equations? How may diff. equations be used? (Modeling) Read: Chapter 1, Section 1.1 In Section 1 (p14 ff) Do Problems +1, 2, +5, 12, +17. Turn in your homework at the start of class on Friday. Also see notes 1 through 5 below.

Note 1)	A "+" mark in front of the problem number means an answer is given at the end of the text, in Appendix D (p755 ff).
Note 2)	If the "Returned" date is a link, then the solution key is posted on Canvas@Dordt. Click on the returned date to go directly to the solution key.
Note 3)	Problem 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 4)	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.
Note 5)	If a link brings you to a login page use your Dordt College network username and password. If this brings you to the opening page of Canvas@dordt instead of the resource you wanted, click your browser's back arrow twice to return to the link on this page, then click the link again. Now that you are signed in the link will work properly.