Mathematical Methods of Physics II
Phys 652 — Spring 2023 
Department of Physics & Astronomy 
Instructor:  Dr. Kevin Beach 
Office:  206 Lewis Hall 
Email:  kbeach@olemiss.edu 
Website:  https://www.phy.olemiss.edu/~kbeach 
Catalog description
Mathematical aspects of the theoretical formulation of classical and modern physics.
3 credit hours
Where and when
Lectures:  T R 9:3010:45 in Lewis Hall Room 104 
Office hours:  by appointment 
Final exam:  Thursday, May 11 at 8:00 
Textbook
Physical Mathematics, Kevin Cahill, Cambridge University Press; 2nd ed. (2019) 
ISBN 9781108470032 [Cambridge University Press] 
Grading scheme
The course grade will be based on the cumulative points earned from weekly assignments, two inclass tests, and a final exam, weighted as follows.
Assignments:  40% 
Inclass tests:  2 × 15% 
Final exam:  30% 
The numerical score (out of 100) will be converted to a letter grade with a corresponding grade point value, following the UM +/– grading system adopted in Fall 2011. The conversion is carried out by matching to the ranges shown in the table below.
Letter grade  Grade point value  Numerical score range 

A  4.0  ≥ 90 
A–  3.7  [85,90) 
B+  3.3  [80,85) 
B  3.0  [75,80) 
B–  2.7  [70,75) 
C+  2.3  [65,70) 
C  2.0  [60,65) 
C–  1.7  [55,60) 
D  1.0  [50,55) 
F  0  < 50 
Class attendance — Regular attendance is strongly encouraged. Some material presented in lecture may not appear in the textbook.
Assignments — The course puts great emphasis on the development of technical mastery in a variety of important mathematical and computational techniques. Students will be regularly asked to attempt problems, both inside and outside of class hours, alone or in groups. Problems assigned as graded homework will be due in class on the designated due date. Late assignments will be penalized at the rate of 20% per day.
Inclass tests — The tentative test dates are listed in this syllabus. Any changes to the dates will be announced in class and by email; students will be given at least one week’s notice. No makeup test will be given except in cases of verified emergencies.
Topics likely to be covered
The twocourse sequence of Phys 651 and 652 will review topics in linear algebra, vector calculus, Fourier series, Fourier and Laplace transforms, complex variables, differential equations, integral equations, special functions, group theory, and probability and statistics. The core of Phys 652 comprises chapters 712 and 1516 of Cahill’s book.
Learning objectives
By the end of the course, students should

know about the various families of differential equations (ordinary and partial, homogeoneous and inhomogeneous, linear and nonlinear, singlevariable and coupled multivariable), their key properties (separability, integrability, exactness), and solution strategies (series solutions, transform methods);

understand the relevance and utility of special functions (Legendre polynomials, cylindrical and spherical Bessel functions) to differential equations and boundary value problems in a highsymmetry context;

recognize the connection between mathematical groups and physical symmetries and understand how to use representations and generators in the solution of physics problems;

be able to apply Bayes’s theorem; be familiar with the distributions most important to physics (binomial, Poisson, Gauss/normal, MaxwellBoltzmann, FermiDirac, BoseEinstein) and how to sample them with random numbers; understand the connection between brownian motion, random walks, and the central limit theorem; and appreciate how these interconnected concepts can be exploited to perform asymptotically exact Monte Carlo calculations.
Schedule
January 23: Classes begin 
T  Jan  24  Lecture 1 
R  Jan  26  Lecture 2 
January 27: Students may add courses on a space available basis through this date 
T  Jan  31  Lecture 3 
R  Feb  2  Lecture 4 
February 3: Last day to register or add classes (between January 28 and February 3 may add only with instructor’s approval); last day for course withdrawals with refund 
T  Feb  7  Lecture 5 
R  Feb  9  Lecture 6 
February 13: Automatic drop date for nonattendance 
T  Feb  14  Lecture 7 
R  Feb  16  Lecture 8 
T  Feb  21  Lecture 9 
R  Feb  23  Lecture 10 
T  Feb  28  Lecture 11 
R  Mar  2  First inclass test 
T  Mar  7  Lecture 12 
R  Mar  9  Lecture 13 
March 10: Deadline for course withdrawals without refund 
March 1119: Spring Break 
T  Mar  21  Lecture 14 
R  Mar  23  Lecture 15 
T  Mar  28  Lecture 16 
R  Mar  30  Lecture 17 
T  Apr  4  Lecture 18 
R  Apr  6  Lecture 19 
April 7: Good Friday holiday 
T  Apr  11  Lecture 20 
R  Apr  13  Lecture 21 
T  Apr  18  Second inclass test 
R  Apr  20  Lecture 22 
T  Apr  25  Lecture 23 
R  Apr  27  Lecture 24 
T  May  2  Lecture 25 
R  May  4  Lecture 26 
May 5: Classes end 
R  May  11  Final examination 
Attendance verification
The university requires that all students have a verified attendance at least once during the first two weeks of the semester for each course. Students whose attendance is not verified will be dropped from the course and any financial aid will be adjusted accordingly. Please see http://olemiss.edu/gotoclass for more information.
Academic integrity and honesty
Students are expected to adhere to the University of Mississippi Creed and the Standards of Honesty as described in Policy Code ACA.AR.600.001 and the M Book.
Students are reminded that cheating in any form will not be tolerated. Performance on all tests and assignments shall represent the individual work of the student. Those who violate the Standards of Honesty will be reported and subject to the appropriate sanction, which may include expulsion from the University.
Nondiscrimination policy
The University complies with all applicable laws regarding affirmative action and equal opportunity in all its activities and programs and does not discriminate against anyone protected by law because of age, color, disability, national origin, race, religion, sex, sexual orientation, handicap, or status as a veteran or disabled veteran.
Policies and procedures for students with disabilities
It is University policy to provide, on a flexible and individual basis, reasonable accommodations to students who have disabilities that may affect their ability to participate in course activities or meet course requirements. Students with disabilities should contact the Office of Student Disability Services (6629157128 or sds@olemiss.edu) to discuss their individual needs.
Examinations and last week of class
Regulations governing all examinations — A student’s failure to appear for an examination without an acceptable excuse, inability to present valid identification, absence from the room during the course of an examination without the consent of the examiner, or attempting any portion of an examination without submitting his or her answers shall result in failure of the examination. Tardiness beyond 15 minutes forfeits a student’s right to an examination.
Final examinations — A final examination, to be given at the time posted in the examination schedule, is required in each undergraduate course, unless the appropriate chair and dean have approved an exception. A student who has three or four final examinations in one day may arrange with the course instructor to take the noon or 7:30 p.m. examination at another time. In order to give a final examination at any time other than that shown in the posted examination schedule, an instructor must have prior approval of the department chair and dean.
Last week of class — The following guidelines exist to allow sufficient time for students and instructors to prepare for final examinations. These guidelines apply to the week preceding final examinations for undergraduate courses held during Fall and Spring semesters.

During the period of Wednesday through Friday of the last week of class, instructors are not to give exams, tests, or quizzes that contribute more than 10% of the final grade for a class.

Exceptions to the above statement are automatically made for labbased courses, technical writing courses, seminar courses that assign a term paper, and senior design courses that assign a multifaceted project in lieu of a final exam. Major projects of the above types, which contribute more than 10% of the final grade and which are due during this Last Week period, should be assigned in the syllabus at the beginning of the semester and any substantial change in the assignment should be made known to students before the drop deadline.
Student support services
The University Counseling Center is a professional facility offered by the University of Mississippi to assist students, faculty, and staff with many types of life stressors that interrupt daytoday functioning, including the stressors associated with the COVID19 pandemic. It offers individual counseling, couples counseling, group counseling, stress management, crisis intervention, assessments and referrals, outreach programs, consultations, and substance abuse services. There is no fee for currently enrolled University students, and anything that students say to a counselor is held in strict confidence. Contact the Counseling Center for information about mental health issues at https://counseling.olemiss.edu, counslg@olemiss.edu, 320 Lester Hall, and https://www.facebook.com/universitycounselingcenterolemiss/. Schedule an appointment or get information about appointments by calling the UCC at 6629153784.
Updated contact information
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