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Privacy Statement & Legal Notices
Office Hours: Fridays 11am - noonish. and by appointment
Course Description: We will study the theory and applications of ordinary differential equations (ODE), the foundations of equations describing how things change: first-order ODE, linear ODE, systems of ODE, obtaining solutions of ODE as series, and the Laplace transform.
Text: Differential Equations and Boundary Value Problems, 4th Edition, Edwards and Penney (ISBN-13: 978-0131561076)
It seems no one has already gotten the 5th edition, so we'll use the 4th edition.
Content: We will cover sections 1.1-1.5, 2.1-2.3, much of chapters 3 and 7, parts of 4,5,6 and maybe a few other things.
Exams: There will be three exams and an OPTIONAL final
(Dates of Exams are subject to change.)
Exam1. Mon Sept 21 Exam2. Mon Oct 26 Exam 3. Mon Dec 7
OPTIONAL Final Mon Dec 14, 2-4:30pm
You will be responsible for the material covered in the lectures, the readings, and the homework.
Homeworks: Homework will be assigned below. It will be due at the beginning of class on Mondays. No late homework will be accepted. Your lowest homework grade will be dropped.
Extra Credit: Occasionally there will be Extra Credit problems worth another point or two on that homework. Turn in Extra Credit problems separately from the rest of your homework.
Grades:
Overall Score = Hwk 25% + Exam1 25% + Exam2 25% + Exam3 25%
If taken, the OPTIONAL Final will take the place of the lowest exam, even if lower.
Letter grades will approximately follow standard cutoffs, e.g. A>90, B>80, C>70 with +/-.
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)
| Week | Readings | Problems due Monday |
|---|---|---|
| Aug 24 | 1.1-1.2 | ***These are from the 4th edition. Due Mon Aug 31. 1.1: # 3, 9, 16, 20, 22, 29, 36, 41, 47 1.2: # 9, 13, 19, 25; (1.1 problems - pdf) (1.2-1.4 problems - pdf.) |
| 1.3-1.4 | Due WEDNESDAY Sept 9 1.3: # 3, 9, 21, 27 (3: y'=y-sin(x) or this, 9: y'=x^2-y-2) 1.4: # 1, 13, 23, 39, 48, 52,
These two might be difficult to read. |
|
| Sept 7 (Labor Day) | 1.5, 1.6 |
Due Mon Sept 14. 1.5: # 11, 21, 32 1.6: # 11, 49, 58, 66, 67 (scans of problems - pdf) We'll delay 1.6: # 23, 35, 37. Notes: 1.6.49 -- Use substitution p=y' as on p73. 1.6.58 -- Use substitution v = ln y as in #57 |
| Sept 14 | 2.1, 2.2 | EXAM 1: Mon Sept 21 Left over problems 1.6: # 23, 35, 37. Extra practice problems: Test1Practice |
| Sept 21 | 2.3, 2.4 |
Due Mon Sept 28. 2.1: # 7, 11, 23, 25; 2.2: # 5, 9, 13, 21, 23, 24; 2.3: # 1, 11 I think you can figure out the two from section 2.3. Read section 2.3 up through Example 2. Extra Credit: Due Mon Oct 5 Describe in your own words what is the (fourth order) Runge-Kutta method for numerically approximating solitions to an initial value problem y'=f(x,y), y(x_0)=y_0. Why can the Euler method and improved Euler method be regarded as first order and second order versions? |
| Sept 28 | 3.1, 3.3 | Due Mon Oct 5 3.1: # 11, 16, 19, 24, 25, 27, 29, 35, 39, 43; |
| Oct 5 | 3.3, 3.5 | Due Mon Oct 12 3.3: # 8, 10, 12, 15, 16, 25, 28, 31, 39, 40, 42 (Capital letters in 40, 42 are unspecified constants.) |
| Oct 12 | 3.4, 3.5, skipping "variation of parameters" |
Due Mon Oct 19 3.4 # 4, 15, 18 3.5: # 1, 4, 6, 10, 13, 18, 34, 37 Deferring 3.6, 3.7 |
| Oct 19 | 3.6, 3.7 | EXAM 2: Mon Oct 26 Practice Exam - pdf Practice Exam Solutions- pdf That's most of them, not all. (Not Due) Spring and Circuit problems: 3.6 # 1, 7, 11 3.7 # 1, 2 |
| Oct 26 | 4.1, 4.2 (pp 247 - 253, 259-260) |
Due Mon Nov 2 4.1 # 17, 26 ; 4.2 # 2 (You may use pplane to sketch direction fields and solution curves.) |
| Nov 2 | 5.2 (pp304 - 308, 311-313) |
Due Mon Nov 9 5.2 # 2, 4, 6, 8, 11, 16 In 8 you'll get complex eigenvalues. Try to do it following pages 311-313. |
| Nov 9 |
6.1, 6.2 (pp 371-374, 384-390) |
Due Mon Nov 16 5.2 # 9, 13 6.1 # 1, 3, 5, 7 (Postponed: 6.2 #21 (phase portrait near origin only), 33) |
| Nov 30 | 6.2, 6.3, 7.1 (pp 384-390, 399-408, 441-445) |
Due Dec 2 6.2 #21 (phase portrait near origin only), 33; 6.3 #14--17 (start reading after problem 13) 27, 29, 31 7.1 #3, 7, 9, 13, 25, 29 |
| Dec 7 | 7.2, 7.3 (pp 452-456, 465-471) |
Exam 3: Mon Dec 7 Optional Final: Mon Dec 14, 2-4:30pm This Table of Laplace Transforms (pdf) will be given to you on both Test 3 and the Final. NOT DUE: Further practice problems. 7.2 #6, 11, 33; 7.3 #3, 6, 8, 37; For Test 3, here is a Practice Exam - pdf. Solutions to some of the problems are here. |