PHYC 366  Mathematical Methods of Physics   Fall 2017


General information          Course overview          Syllabus          Tentative schedule          Problems and Assignments          Exams


General information


Tuesday and Thursday, 11:00-12:15, and Friday 11:00-11:50, P&A 184

Lectures (PHYC 366.001):

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.

Instructor:

Anthony Demme

office: P&A front area,   email: ademme_at_unm.edu,   office hours: Thursday 15:30-17:30

Teaching Assistant:

Mary L. Boas, "Mathematical Methods in the Physical Science," 3rd Edition, Wiley (required)

Textbook:



Course overview


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. 



Syllabus

The textbook provides materials enough for a year-long course, so it is expected that we can only cover the following topics.

2. Complex numbers   [Lecture note on the chapter 2]

3. Linear algebra   [Lecture note on the chapter 3]

6. Vector analysis   [Lecture note on the chapter 6]

7. Fourier series and transforms   [Lecture note on the chapter 7]

13. Partial differential equations   [Lecture note on the chapter 13]



Tentative schedule

Last updated on November 17, 2017

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

Nov. 23  Thu
Thanksgiving holidays

Nov. 24  Fri
Thanksgiving holidays
Nov. 28  Tue
13.5

Nov. 30  Thu


Dec. 1  Fri


Dec. 5  Tue


Dec. 7  Thu


Dec. 8  Fri


Dec. 11-15
final week




Problems and Assignments


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]




Exams


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]