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Office Hours: Wednesdays, 1-3pm
Course Description: We will study the theory and applications of ordinary differential equations (ODE): first-order ODE, linear ODE, obtaining solutions of ODE as series, the Laplace transform.
Text: Differential Equations and Boundary Value Problems, 4th Edition, Edwards and Penney
Content: We will cover sections 1.1-1.5, 2.1-2.3, much of chapters 3 and 7, parts of 4,5,6.
Exams: There will be two exams and a final.
Exam1. Thurs Sept 26 Exam2. Thurs Nov 14 Final. Tues Dec 17th 5-7:30 pm
You will be responsible for the material covered in the lectures, the readings, and the homework.
* Dates of Exam1 and Exam2 are subject to change.
Homeworks: Homework will be assigned below. It will be due at the beginning of class on (non-exam) Thursdays. No late homework will be accepted. Your lowest homework grade will be dropped.
Grades: Overall Score = Hwk 25% + Exam1 25% + Exam2 25% + Final 25%
Letter grades will approximately follow standard cutoffs A>90, B>80, C>70.
Academic Honesty: Each student will uphold the University of Miami Honor Code.
Math Lab Schedule (Free drop-in tutoring)
dfield and pplane - Java applets for direction fields and phase portraits
Example outputs as pdfs: y'=x^2-y^2 ; y'=x^2-y-2 ; y'=y-sin(x) ; x' = t * sin(x)
| Due Date | Readings | Problems |
|---|---|---|
| Aug 29 | 1.1 | 1.1: # 3, 9, 15, 19, 22, 47 (scans of problems - pdf) |
| Sept 5 | 1.2-1.5 | 1.2: # 9, 13, 19, 25; 1.3: # 3 (y'=y-sin(x), see also this), 9 (y'=x^2-y-2), 21, 27 1.4: # 1, 13, 23, 64; (scans of problems - pdf) 1.4.13: y^3 dy/dx=(y^4+1)cos x, 1.4.23: dy/dx + 1 = 2y, y(1)=1 |
| Sept 12 | 1.6, 2.1, 2.2 | 1.5: # 11, 21; 1.6: # 11, 23, 35, 49 (not due, but worth a look: 66, 67) 2.1: # 7, 11, 23, 25; (2.2 Deferred to next week) Exact Equation Plots (Mathematica) |
| Sept 19 | 2.2, 2.3, 2.4 | 2.2: # 5, 9, 13, 21, 23, 24; 2.3: # 1, 11, 15, 16; 2.4: # 3, 5 Growth and Logistics (Mathematica) |
| Sept 26 | 3.1 | Exam 1 on Thursday Practice Problems - pdf |
| Oct 3 | 3.1, 3.3 | 3.1 # 11, 16, 24, 25, 35, 39, 43 3.3 # 10, 12, 15, 25, 31, 40, 42 |
| Oct 10 | 3.5 | 3.5 # 1, 4, 6, 10, 13, 18, 34, 37 |
| Oct 17 | 3.4, 3.6, 3.7 (pp 212-216, 219-221, 225 - 231) |
Fall Break |
| Oct 24 | 4.1, 4.2 (pp 250 - 253, 259-260) |
3.4 # 4, 15, 17, 18 3.6 # 1, 7, 11, 19; 3.7 # 1, 2, 17 4.1 # 17; 4.2 # 2 |
| Oct 31 | 5.2, 5.4 (pp304 - 308, 311-313, 334 - 337) |
Solve the systems and sketch the phase portraits. 5.2 # 4, 6, 8, 11; |
| Nov 7 |
6.1 (pp 371-374) 4.3 (pp 269 - 271) |
5.4 # 1,5 6.1 #1, 3, 5, 7 4.3 #1(a), 5(a) for both, compare with actual solutions (Here's the Mathematica file from class StreamPlots) |
| Nov 14 | 6.2, 6.3; (pp 384-390, 399-408) | Exam 2 on Thursday Some practice problems from the book (not due): 6.2 #21 (phase portrait near origin only), 33; 6.3 #27, 29, 31 (phase portrait only); Practice Exam Problems - pdf |
| Nov 21 | 7.1 (pp 441-445) | 7.1 #3, 13, 25, 29; |
| Nov 28 | 7.2 | Thanksgiving Break |
| Dec 10 | 7.2, 7.3, 7.5, 7.6 (pp 452-56, 465-471, 482-488, 494-498) |
7.2 #6, 33;
7.3 #3, 6, 8, 37; 7.5 #13, 26; 7.6 #5 Due Dec 10 |
| Dec 17 |
The exam will focus upon what we've been doing with the Laplace Transform, but you can also expect to
For the exam, I'll be giving you the first page of This Table. |