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| Lecture Room: | 115 Van Hise |
| Lecture Time: | 11:00–12:15 TuTh |
| Lecturer: | Jean-Luc Thiffeault |
| Office: | 503 Van Vleck |
| Email: |
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| Office Hours: | Tue 12:15–13:00, Thu 8:30–9:15 |
The final is Wednesday December 19, 2018 at 12:25–14:25.
See the official syllabus.
The textbook for the class is Applied Partial Differential Equations by Richard Haberman.
The current edition is the Fifth, but you can use earlier editions if you find them for cheaper. (Earlier edition might be missing a bit of material, so you can use the copy on reserve in the library for reference in those cases.)
Math 319 and 321.
Every two weeks or so I will assign homework from the textbook (or other sources) and post it here. The homework will be due in class about two weeks later.
| homework | due date | problems |
| 1 | 09/25 | 1.2: 3,5; 1.3: 1,2; 1.4: 1(bceg),2,5,10; 1.5: 1,3,5,12,18,19,22,23. |
| 2 | 10/09 | 2.2: 2,3,4; 2.3: 1(bd),2(aceg),3(ab),4,5,7,11; 2.4: 1,2,3,4. |
| 3 | 10/23 | 2.4: 6(b); 2.5: 1(bg),2,3(a),5(b),8(b),12; 3.3: 2(c),4,5(a),7,15. 3.4: 9,11; 3.5: 1; 3.6: 2; |
| 4 | ||
| 5 | 4.2: 1; 4.4: 3,7,9,10. 5.3: 2,3,8,9; 5.4: 1; 5.5: 1(de),8; 5.8: 1,6,9,11. 7.2: 2; 7.3: 1(e),4(a),7(b); 7.7: 2(a),3,7. 7.8: 2; 7.9: 1(d),3(a),4(b); 7.10: 2(bd),9(d); | |
| 6 | 04/15 | 8.2: 1(bf),2(d),3,5,6(b); 8.3: 1(ae),6; 9.2: 4(ab); 9.3: 1,3,4,11,12(b),21,23. |
There will be a midterm exam and a cumulative final exam. The final grade will be computed according to:
| Homework | 35% |
| Midterm exam | 30% |
| Final exam | 35% |
The midterm exam will be given in class on the date below.
| Midterm exam | Tue Oct 30, 2018 at 11:00–12:15 | (in class) |
| Final exam | Wed Dec 19, 2018 at 12:25–14:25 | (room SOC SCI 6240) |
We'll use Canvas discussions about the class and related topics. Feel free to post questions and answers there about homeworks and exams, logistics, or relevant interesting things you found on the web.
Note: there is not necessarily a one-to-one correspondence between lectures numbers and dates.
| lecture | date(s) | sections | topic |
| 1 | 09/06 | 1.1–1.2 | Heat equation |
| 2 | 09/11 | 1.3–1.4 | Boundary conditions; Equilibrium distribution |
| 3 | 09/13 | 1.5 | Higher dimensions |
| 4 | 09/18 | 2.1–2.3 | Linearity; Separation of vatiables |
| 5 | 09/20 | 2.3 | Separation of variables (cont'd) |
| 6 | 09/25 | 2.3.6; Appendix to 2.3 | Separation of variables (cont'd) |
| 7 | 09/27 | 2.4 | Separation of variables (cont'd) |
| 8 | 10/02 | 2.5 | Laplace's equation |
| 9 | 10/04 | 2.5.2 | Laplace's equation in a disk |
| 10 | 10/09 | 2.5.4 | Mean value theorem; Maximum principle; Uniqueness |
| 11 | 10/11 | 3.1–3.3 | Fourier series; Sine and cosine series |
| 12 | 10/16 | 3.4–3.6 | Differentiation and integration of Fourier series; Complex form |
| 13 | 10/18 | 4.1–4.5 | Wave equation |
| 14 | 10/23 | 5.1–5.4 | Sturm–Liouville eigenvalue problems |
| 15 | 10/25 | 5.5 | Sturm–Liouville proofs |
| – | 10/30 | – | Midterm [mean 80.6%; solutions] |
| 16 | 11/01 | 5.6–5.8 | Rayleigh quotient; Sturm–Liouville example |
| 17 | 11/06 | 7.1–7.5 | Higher-dimensional PDEs |
| 18 | 11/08 | 7.7–7.8 | Vibrating circular membrane; Bessel functions |
| 19 | 11/13 | 7.9 | Laplace's equation in a cylinder |
| 20 | 11/15 | 7.10 | Spherical coordinates; Legendre polynomials |
| 21 | 11/20 | – | Cooking by flipping |
| 22 | 11/27 | 8.1–8.5 | Nonhomogeneous problems; Resonance |
| 23 | 11/29 | 9.1–9.3 | Green's functions |
| 24 | 12/04 | 9.4 | Green's functions (cont'd) |
| 25 | 12/06 | 9.5.5–9.5.6 | Green's functions (cont'd) |
| 26 | 12/11 | – | The heat equation and probability |
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Last modified: 19:39 1 April 2021 |
Background: Coarsening of a binary fluid (Simulations by Lennon Ó Náraigh) |
Follow @jeanluc_t |
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