Tuesday and Thursday, 11:00-12:15, and Friday 11:00-11:50, P&A 184
Professor Akimasa Miyake
office: P&A 25, email: amiyake_at_unm.edu, office hours: Tuesday 13:30-15:30, otherwise you may arrange a meeting by appointment.
Anthony Demme
office: P&A front area, email: ademme_at_unm.edu, office hours: Thursday 15:30-17:30
Mary L. Boas, "Mathematical Methods in the Physical Science," 3rd Edition, Wiley (required)
The purpose of this course is to introduce students to two important areas of mathematical physics, linear algebra and partial differential equations (PDEs), because of their ubiquitous applications to physical problems in mechanics, E&M, and quantum mechanics at the upper-division undergraduate level. This class will provide a physics-based coverage of these mathematical areas in contrast to the more traditional linear algebra and PDE classes offered by the Mathematics department. The course prerequisites are officially PHYC 290 and MATH 316 (otherwise, students may discuss their enrollment with the instructor). The course is suitable for undergraduate students (mainly the physics and astrophysics majors) to prepare their mathematical background needed to tackle junior and senior level physics classes, based on the foundational concepts of complex numbers, vector analysis, and ordinary differential equations.
We adapt modern pedagogy of active learning in classroom. It is quite important to do exercise, in order to digest notions and methods learned in the lectures. Furthermore, the problems of homework assignments will be selected largely from the exercises of the textbook in accordance with the progress of lectures. The final grade will be determined based on performance of exams and assignments (their weights are 70 % and 30 % respectively, for now). Each mid-term exam is arranged after a couple of chapters are completed. That is how you can study rather narrow, clearly-defined selections of materials for every exam, while they are still fresh in your mind. Overall it is expected that your learning is more effective and at the same time the load by the course is less stressful this way.
Dates |
Subjects |
Assignments |
Aug. 22 Tue |
2.1-2.5 |
2.4: 4, 6, 11, 17, 20 2.5: 19, 22, 23 |
Aug. 24 Thu |
2.5-2.7 | 2.5:
36, 46, 55, 62 2.6: 2, 6, 12 |
Aug. 25 Fri |
2.8 |
2.7: 3, 10 2.8: 1, 3 |
Aug. 29 Tue |
2.9-2.11, taught by Dr. Jackson |
2.9: 4, 18, 19, 27 2.10: 6, 18, 24, 28 2.11: 17, 18 |
Aug. 31 Thu |
2.12-2.15, taught by Dr. Jackson | 2.12: 1, 11, 22 2.14: 1, 11 2.15: 6, 13 |
Sep. 1 Fri |
2.16, taught by Dr. Jackson | 2.16: 6, 8 Calculate |e^(-iw1t)+e^(-iw2t)|^2 and describe some corresponding physics |
Sep. 5 Tue |
3.1-3.3 |
3.2: 1, 11, 17 |
Sep. 7 Thu |
3.3-3.4 |
3.3: 3, 7, 13 |
Sep. 8 Fri |
3.4 |
3.4:
2, 9, 15, 21, 23 |
Sep. 12 Tue |
3.5 |
3.5: 12, 16, 30, 33 |
Sep. 14 Thu |
3.6-3.7 |
3.6: 2, 6, 15, 19, 32 |
Sep. 15 Fri |
3.7 |
Derive the orthogonal matrix for active rotations in 2D |
Sep. 19 Tue |
3.7-3.8 | 3.7: 2, 5, 19, 28, 31 |
Sep. 21 Thu |
3.8-3.11 | 3.8: 1, 5, 6, 11, 25 |
Sep. 22 Fri |
3.11 | no
homework |
Sep. 26 Tue |
3.11-3.12 | 3.10:
2 3.11: 6, 18, 36, 47, 52 |
Sep. 28 Thu |
3.13 |
3.12: 2, 8, 16 3.13: 1, 3, 6 |
Sep. 29 Fri |
6.1-6.3 |
no homework |
Oct. 3 Tue |
6.3-6.4 |
6.3: 4, 12, 16 Derive the acceleration of a constant-speed rotation on a circle, using differential formulas |
Oct. 5 Thu |
6.5-6.6 |
6.4: 1, 2, 6 |
Oct. 6 Fri |
6.6-6.8 |
6.6: 5, 8, 11, 21 Exercise Example 1 in page 300 |
Oct. 10 Tue |
6.8-6.9 |
6.7: 11, 19, 20 6.8: 2, 11, 20 |
Oct. 12 Thu |
Fall break | |
Oct. 13 Fri |
Fall break |
|
Oct. 17 Tue |
6.9-6.10 | 6.9:
4, 6, 7 Exercise Example in page 319 |
Oct. 19 Thu |
6.10-6.11 |
6.10: 1, 9, 13 Exercise Example 1 in page 328 |
Oct. 20 Fri |
6.11 |
6.11:
4, 5, 16 |
Oct. 24 Tue |
mid-term exam 10:45-12:30 |
|
Oct. 26 Thu |
7.1-7.5 |
7.2: 5, 17, 23 7.4: 1, 2, 7 |
Oct. 27 Fri |
7.5 |
7.5: 7 7.6: 14 |
Oct. 31 Tue |
7.5-7.9 |
7.7: 7 7.8: 11 |
Nov. 2 Thu |
7.9-7.11 |
7.9: 23 7.10: 4 7.11: 4, 11 |
Nov. 3 Fri |
7.12 |
7.12: 3, 17, 23 |
Nov. 7 Tue |
13.1-13.2 |
13.1: 2, 4 |
Nov. 9 Thu |
13.3 |
13.2: 5, 10, 11(hint in page
625) |
Nov. 10 Fri |
13.3 |
no homework |
Nov. 14 Tue |
13.3 |
13.3: 3, 7(hint in page
631), 11 |
Nov. 16 Thu |
13.3-13.4 |
no homework |
Nov. 17 Fri |
13.4 |
13.4: 5, 8 |
Nov. 21 Tue |
13.5 |
10.9: 16, 18 |
Nov. 23 Thu |
Thanksgiving
holidays |
|
Nov. 24 Fri |
Thanksgiving holidays | |
Nov. 28 Tue |
13.5 |
10.9: 17, 19 |
Nov. 30 Thu |
13.5 |
no homework |
Dec. 1 Fri |
13.5 |
13.5: 9, 11 13.6: 6 |
Dec. 5 Tue |
13.5 |
13.5: 1, 4 |
Dec. 7 Thu |
13.7 |
13.7: 2, 13 |
Dec. 8 Fri |
13.7 |
no homework |
Dec. 11-15 |
final
week |
Students may study subjects of assignments together, but everyone is expected to prepare his/her original answer sheets.
1. Assignment: [Problems of Sections 2.4-2.8 Solutions]
2. Assignment: [Problems of Sections 2.9-2.16 Solutions]
3. Assignment: [Problems of Sections 3.1-3.4 Solutions]
4. Assignment: [Problems of Sections 3.5-3.6 Solutions]
5. Assignment: [Problems of Sections 3.7-3.8 Solutions]
6. Assignment: [Problems of Sections 3.10-3.13 Solutions]
7. Assignment: [Problems of Sections 6.3-6.6 Solutions]
8. Assignment: [Problems of Sections 6.7-6.8 Solutions]
9. Assignment: [Problems of Sections 6.9-6.11 Solutions]
10. Assignment: [Problems of Sections 7.2-7.6 Solutions]
11. Assignment: [Problems of Sections 7.7-7.12 Solutions]
12. Assignment: [Problems of Sections 13.1-13.2 Solutions]
13. Assignment: [Problems of Sections 13.3-13.4 Solutions]
14. Assignment: [Problems of Sections 10.9 Solutions]
15. Assignment: [Problems of Sections 13.5 Solutions]
16. Assignment: [Problems of Sections 13.7 Solutions]
Mid-term exams are usually held during the Friday problems session in a closed-book format. No communication with other students is allowed during the exams.
1. Mid-term exam, 10:45-12:30 on October 24 (Tue) [Materials from Chapters 2, 3, 6 Solutions and grading rubric]
2. Final exam, 12:30-15:00 on December 12 (Tue), P&A 184 [Materials from Chapters 7, 13 (until 13.7) Solutions and grading rubric]