Intro to Differential Equations — §101, Fall, '13 (134)
| Let us reflect that, having banished from our land that religious intolerance under which mankind so long bled and suffered, we have yet gained little if we countenance a political intolerance as despotic, as wicked, and capable of as bitter and bloody persecutions. |
| — Thomas Jefferson (1743-1826) in his First Inaugural Address. |
Homework List
✈ Jump down to '♞ This Week.'
Week 1
- Tuesday, Aug 20 — First day of classes
- Wednesday, Aug 21
◊ Read the Course Information pages.
§1.1, pg. 13. No. 1, 2, 5, 10a, 19, 21.
- Friday, Aug 23
§1.2, pg. 31. No. 1, 4, 5, 10, 11, 15, 24, 34, 35.
Week 2
- Monday, Aug 26 — Last day to drop/add classes
§1.3, pg. 46. No. 1, 5, 8, 9, 11, 14, 15.
- Wednesday, Aug 28
§1.4, pg. 62. No. 1 (by hand), 5, 11.
◊ A Maple Euler's method worksheet
is in the ClassNotes directory.
- Friday, Aug 30
§1.5, pg. 71. No. 1, 4, 5→8, 10, 15.
¤ Quiz on Chapter 1 next Friday.
Week 3
- Monday, Sept 2 — Labor Day holiday; no classes
- Wednesday, Sept 4
§1.6, pg. 88. No. 1, 3, 5, 12, 16, 19, 20, 25, 31.
- Friday, Sept 6
¤ Quiz today!
§1.7, pg. 104. No. 1→5 (also draw bifurcation diagrams for each DE), 9.
◊ A Maple bifurcation diagram worksheet
is in the ClassNotes directory.
Week 4
- Monday, Sept 9
§1.8, pg. 115. No. 1, 3, 7, 14, 20.
¤ Assume the approximate volume in a bay is four million liters. Further assume that polluted water flows into the bay at a rate of \(40,\!000\) liters per day, and that the water flows out of the bay at the same rate.
- Write a differential equation that models the concentration of pollutants in the bay. Include a boundary condition if the bay begins with \(N\) milligrams per liter of pollutants. Explain your model.
- The amount of pollutants \(Q(t)\) will be measured in milligrams and the concentration \(C(t)\) will therefore have units of milligrams per liter. Time will be measured in days. The bay begins with \(0.8\) milligrams of pollutants per liter of water. The stream normally has a pollution concentration of \(k = 0.5\) milligrams per liter.
Find the concentration of the pollutants in the bay for the first thirty days.
- Wednesday, Sept 11
◊ Read CDR Harrison Schramm's "Five-Minute Analyst: Modeling Zombies". (CDR Schramm is a member of ASU's COMAP Modeling Contest triage grading team.)
§1.9, pg. 127. No. 1, 2, 3, 7, 19.
- Friday, Sept 13
¤ Lab 1.1 report is due by 5:00 pm Monday, 9/16.
Week 5
- Monday, Sept 16
§2.1, pg. 151. No. 1, 2, 7, 9, 16, 19.
¤ You can find applets online to draw slopefields and phase portraits:
◊ It's time to start thinking about our first test...
- Wednesday, Sept 18
§2.2, pg. 169. No. 1→ 6, 7, 16, 17→ 20, 21, 23.
- Friday, Sept 20
§2.4, pg. 196. No. 1, 3, 5, 7.
Week 6
- Monday, Sept 23
◊ Start making your note sheet (8.5"×11") for Test 1.
§2.5, pg. 204. No. 1, 2, 4ef, 5.
- Wednesday, Sept 25
¤ Chapter 1 Review, pg. 136.
¤ Chapter 2 Review, pg. 234.
- Friday, Sept 27
¤ Study for the test!
Week 7
- Monday, Sept 30
◊ Test 1 is today!
- Wednesday, Oct 2
§3.1, pg. 258. No. 1, 5, 7, 11 (with Maple), 19, 24.
- Friday, Oct 4
§3.2, pg. 277. No. 1, 12ab, 15, 17, 19abc, 21.
Week 8
- Monday, Oct 7
§3.5, pg. 327. No. 1→9 odd.
- Wednesday, Oct 9
§3.3, pg. 293. No. 1→9 odd, 17, 18, 19.
- Friday, Oct 11
¤ Chapter 3 Review, pg. 376.
Week 9
- Monday, Oct 14
◊ Quiz today!
- Wednesday, Oct 16
§5.1, pg. 417. No. 1, 2, 3.
- Thursday & Friday, Oct 17-18
◊ No classes — Fall Break! So go explore Explore.org.
Week 10
- Monday, Oct 21
§5.2, pg. 432. No. 1, 5, 9, 21.
¤ Duffing oscillator Maple worksheet.
- Wednesday, Oct 23
§5.2, pg. 432. No. 15, 19.
¤ Nonlinear example from class Maple worksheet.
- Thursday, Oct 24 — Last day to drop any course.
- Friday, Oct 25
¤ The Hard And Soft Spring Project. Due Monday, Oct 28 Tuesday, Oct 29.
¤ Chapter 5 Review, pg. 555.
Week 11
- Monday, Oct 28
§6.1, pg. 577. No. 1→6, 9, 11, 15.
¤ See the Laplace Transform Table
- Wednesday, Oct 30
§6.1, pg. 577. No. 7→14.
- Friday, Nov 1
¤ Quiz next Friday! (11/8)
§6.2, pg. 586. No. 1→5, 9, 11, 14.
Week 12
- Monday, Nov 4
§6.3, pg. 599. No. 1, 7→9, 11, 15, 23, 29.
- Tuesday, Nov 5
¤ Election day in Boone.
- Wednesday, Nov 6
◊ It's time to start thinking about our next test...
§6.4, pg. 539. No. 3, 5, 7.
- Friday, Nov 8
¤ Quiz Today! (on Laplace transforms)
◊ Read §6.5
Week 13
- Monday, Nov 11
¤ Chapter 6 Review, pg. 627.
§7.1, pg. 644. No. 1.
- Wednesday, Nov 13
§7.1, pg. 644. No. 3, 5, 7.
- Friday, Nov 15
¤ Test next Mōnandœg!
◊ You can bring:
- Calculator (check the batteries)
- Two sheets (8½"×11") of notes
Note: The Laplace transform table will be printed with the test; you don't need to bring it.
Week 14
- Monday, Nov 18
¤ Test 2 is today!
- Wednesday, Nov 20
§7.2, pg. 654. No. 3, 5, 17.
¤ Let \(y^{\prime} = y^2-y^3,\quad y(0)=0.2,\quad t_0=0,\quad t_n=10,\quad \text{and } n=100\).
- Use Euler's method in Maple to calculate \(y_n=y(t_n)\).
- Use Heun's method in Maple to calculate \(y_n=y(t_n)\).
- Compare your answers.
- Friday, Nov 22 — Remembrance of President John F. Kennedy.
§7.3, pg. 664. No. 6, 7, 8.
¤ Use Maple to apply each of the methods — Euler's, Heun's, and RK4 — to the initial value problem
\[ y^\prime = 9\,y\cdot(1-y), \quad y_0 = 1.25 \]
to calculate \(y(10)\) beginning with \(h = 0.29\).
Week 15
Week 16
Week 17 — Final Exam Week
♞ (This Week)
- Tuesday, Dec 11
◊ Office Hours: 1:00 to 3:00 pm
- Friday, Dec 13
¤ Final Exam: 3:00 - 5:30 pm
☞ You can bring:
- Calculator (check the batteries)
- Any notes; no books or people.
| “Don't just read it; fight it! Ask your own questions, look for your
own examples, discover your own proofs. Is the hypothesis necessary? Is the
converse true? What happens in the classical special case? What about the
degenerate cases? Where does the proof use the hypotheses?”
|
|
— Paul Halmos
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Last modified: Wednesday, 01-Feb-2023 08:32:11 EST
