| Course number: | MATH-UA 262-003 |
| Semester: | Fall 2019 |
| Time & location: | Mon & Wed, 9:30am - 10:45am in CIWW 312 |
| Instructor: | Mike O'Neil (oneil@cims.nyu.edu) |
| Office hours: | Thu, 11:00am - 12:00pm in CIWW 1119 (or by appointment) |
| Recitation time & location: | Fri, 3:30pm - 4:45pm in CIWW 201 |
| Instructor: | Vismayie Vandanapu (vv846@nyu.edu) |
| Office hours: | Fri, 4:45pm - 5:45pm in CIWW 230 |
This is a first course in ordinary differential equations which will cover analytical solution methods, elementary numerical methods, and modeling. Topics to be covered include: first-order equations including integrating factors; second-order equations including variation of parameters; series solutions; elementary numerical methods including Euler's methods, Runge-Kutta methods, and error analysis; Laplace transforms; systems of linear equations; boundary-value problems. Some optional topics to be chosen at the instructor's discretion include: nonlinear dynamics including phase-plane description, elementary partial differential equations, and Fourier series.
The textbook for the course is Martin Braun, Differential Equations and Their Applications, 4th Edition, 1993.
The textbook is available for free (electronically)
to NYU students on SpringerLink at:
http://proxy.library.nyu.edu/login?url=https://link.springer.com/book/10.1007/978-1-4612-4360-1.
Overall numerical grades will be computed from homework (10%), two midterm exams (25% each), and one final exam (40%). The final letter grade will be determined from the overall numerical grade.
Homework will be assigned weekly on Monday (usually posted here after class) and due the following Monday at the beginning of class. No late homework is accepted without prior approval from the instructor, and in those cases, generally exemptions will only be made for medical reasons with documentation. Students are encouraged to work together on their homework, but each student must write-up and submit the assignments independently.
| Item | Due date | Materials | Mean | Stdev | Median |
|---|---|---|---|---|---|
| HW 1 | Sep 16 | Braun 1.2: 6, 12, 18 Braun 1.4: 6, 20 |
19.81 | 5.12 | 21.25 |
| HW 2 | Sep 23 | Braun 1.8: 14, 16 Braun 1.9: 4, 10, 12, 16 Braun 1.10: 2 |
21.34 | 6.66 | 24 |
| HW 3 | Sep 30 | Braun 1.10: 6, 10, 18 Braun 1.11.1 (page 91): 2 Braun 1.13: 2, 4 |
20.99 | 7.28 | 24 |
| Exam 1 | Oct 2 | 37.4 | 8.1 | 39 | |
| HW 4 | Oct 15 | Braun 2.1: 6, 10, 12, 14 Braun 2.2: 4, 6, 10 Braun 2.2.1: 6, 8, 10 |
23.84 | 2.35 | 25 |
| HW 5 | Oct 21 |
Braun 2.2.2: 2, 6, 14, 18 Braun 2.3: 2, 4 Braun 2.4: 4, 6, 10 |
22.95 | 5.47 | 25 |
| HW 6 | Oct 28 |
Braun 2.8: 4, 8, 10, 12 Braun 2.8.1: 2, 6, 8 |
20.01 | 5.2 | 21.5 |
| HW 7 | Nov 4 |
Braun 2.8.2: 4, 8, 12, 24 Braun 2.9: 6, 8, 16, 20 Braun 2.10: 4, 12, 22 |
|||
| Exam 2 | Nov 6 | 35.89 | 9.12 | 37 | |
| HW 8 | Nov 18 |
Braun 3.1: 2, 4 Braun 3.2: 2, 6, 10 Braun 3.3: 2, 4, 10 Braun 3.4: 2, 6 |
24.31 | 1.63 | 25 |
| HW 9 | Nov 25 |
Braun 3.8: 2, 10, 18 Braun 3.9: 2, 6 Braun 3.10: 8, 10, 16 |
20.98 | 8.12 | 25 |
| HW 10 | Dec 9 |
Braun 4.1: 4, 6, 8 Braun 4.2: 4, 8 Braun 4.3: 2, 4, 14, 16 |
|||
| HW 11 | Not collected | Braun 4.4: 2, 8, 11, 14 Braun 4.7: 2, 6, 8, 10 Braun 5.1: 2, 4, 7, 8, Braun 5.3: 4, 8, 10 Braun 5.4: 2, 8, 12, 16 Braun 5.5: 2, 10 |
Below is an updated list of discussion topics along with any documents that were distributed, notes, or relevant code.
| Date | Topics | Materials |
|---|---|---|
| Sep 4 | Intro to the course, 1st order equations | Braun 1.1-1.2 Lecture notes |
| Sep 9 | Integrating factors, separable equations | Braun 1.2-1.4 Lecture notes |
| Sep 11 | Separable equations, orthogonal trajectories, exact equations |
Braun 1.4, 1.8, 1.9 Lecture notes |
| Sep 16 | Exact equations | Braun 1.9 Lecture notes |
| Sep 18 | Existence and uniqueness | Braun 1.10 Lecture notes |
| Sep 23 | Euler's method | Braun 1.13, 1.13.1 Lecture notes |
| Sep 25 | Newton's method, 2nd order equations | Braun 1.11.1, 2.1 Lecture notes |
| Sep 30 | 2nd order equations, review | Braun 2.1 Lecture notes |
| Oct 2 | Prelim exam 1 | |
| Oct 7 | 2nd order equations | Braun 2.1, 2.2 Lecture notes |
| Oct 9 | Complex and repeated solutions | Braun 2.2, 2.2.1, 2.2.2 Lecture notes |
| Oct 14 | NO CLASS | |
| Oct 15 | CLASS!!! Variation of parameters | Braun 2.3, 2.4 Lecture notes |
| Oct 16 | Series solutions | Braun 2.8 Lecture notes |
| Oct 21 | Singular ODEs | Braun 2.8, 2.8.1, 2.8.2 Lecture notes |
| Oct 23 | Singular ODEs | Braun 2.8.2, 2.8.3 Lecture notes |
| Oct 28 | Laplace transforms | Braun 2.9, 2.10 Lecture notes |
| Oct 30 | Class cancelled | |
| Nov 4 | Review | |
| Nov 6 | Prelim exam 2 | |
| Nov 11 | Systems of DEs | Braun 3.1-3.4 Lecture notes |
| Nov 13 | Eigenvector solutions | Braun 3.8 Lecture notes |
| Nov 18 | Complex roots | Braun 3.9 Lecture notes |
| Nov 20 | Repeated roots, matrix exponential | Braun 3.10 Lecture notes |
| Nov 25 | Qualitative theory | Braun 4.1-4.3 Lecture notes |
| Nov 27 | THANKSGIVING - NO CLASS | |
| Dec 2 | Equilibria, stability | Braun 4.1-4.3 Lecture notes |
| Dec 4 | Phase portraits | Braun 4.4, 4.7 Lecture notes |
| Dec 9 | Two-point BVPs, separation of variables |
Braun 5.1-5.3 Lecture notes |
| Dec 11 | Fourier series | Braun 5.4-5.5 Lecture notes |
| Dec 18 | FINAL EXAM 8am-9:50am, CIWW 312 |