Mathematical Physics

PHY 365 --- Spring 2010 Syllabus

Physics Department --- Mercer University


Texts: (RHB, required) Mathematical Methods for Physics and Engineering, 3rd edition, 
     by K. F. Riley, M. P. Hobson, and S. J. Bence
     and (AW, suggested) Mathematical Methods for Physicists, 6th edition,
     by George B. Arfken and Hans J. Weber.

 Class meetings: T 6:00-7:15pm, F 3:00-4:15pm, SEB 140
Instructor: Dr. Jose L. Balduz Jr.


          office: SEB 205,  phone: 478-301-2229

          office hours: M 2-4pm, W 1-3pm, R 12-1pm or by appointment...



This is an advanced course in mathematical methods in the physical sciences, for junior or senior level students. It is intended primarily for physics majors, but should be of interest also to many other students, especially those in the sciences and engineering. The course prerequisites are
    PHY 161 & 162 General Physics I & II
    MAT 293 Multivariable Calculus
, and 
    MAT 330 Introduction to Differential Equations

Students are therefore assumed to know basic college physics, and to be familiar with partial differentiation and  ordinary differential equations.


Students will have the opportunity to learn theory and applications, in a physics context, of some the following mathematical tools: vector algebra and calculus, probability distributions, matrix algebra and normal modes, systems of linear ordinary differential equations, linear algebra and group theory as applied to coordinate transformations, Fourier analysis and orthogonal functions, solutions to partial differential equations, the calculus of variations, and tensor algebra. The goal is for students to acquire techniques beyond those of basic calculus, multivariable calculus, and ordinary differential equations, which they may use to perform nontrivial analysis and calculations in their advanced physics and other courses.


This course enrolls a small number of students, with a variety of backgrounds and interests. This will afford the opportunity to specialize the course to some extent for each student. Some topics will be in common for all students, with common homework assignments and a final exam. Beyond that each student will choose, in consultation with the instructor, an additional set of topics to study. Special homework assignments will be given to each student in their special topics, and each student will carry out a course project in this area.


The common topics will be

(RHB) Ch.  8.  Matrices and Vector Spaces

(RHB) Ch.  9. Normal Modes
(RHB) Ch. 12.  Fourier Series
(RHB) Ch. 13.  Integral Transforms (1, Fourier Transforms)

(RHB) Ch. 17.  Eigenfunction Methods for Differential Equations (1-6)
and (AW) Ch. 4.  Group Theory (Lie Groups: Rotations, Lorenz Group, Unitary Groups).


Some likely special topics for student choice include (But see also (AW) or other texts.)
(RHB) Ch. 7.  Vector Algebra
(RHB) Ch. 10.  Vector Calculus

(RHB) Ch. 11.  Line, Surface, and Volume Integrals
(RHB) Ch. 15.  Higher-Order Ordinary Differential Equations
(RHB) Ch. 16.  Series Solutions of ODEs

(RHB) Ch. 18.  Special Functions

(RHB) Ch. 19.  Quantum Operators
(RHB) Ch. 21.  Partial Differential Equations: Separation of Variables and Other Methods
(RHB) Ch. 22.  Calculus of Variations
(RHB) Ch. 26.  Tensors

(RHB) Ch. 27.  Numerical Methods

(RHB) Ch. 30.  Probability.


Lectures (2 hours/week): Class time will be devoted mostly to conventional lectures, including theory and examples. We will also discuss the material and go over problems in the text, including homework.


Tutorials (1 hour/week): Additional time beyond lectures must be spent by each student working with the instructor on their special topics, up to one hour per week. Towards the end of the semester, this may be replaced by short class presentations by each student on their special topics projects.


Common Topics (75% of total grade):
Homework (60%):  For each common topic the instructor will assign some homework problems to be worked by the students and handed in for grading. There will be about eight homework sets. Students are free to collaborate on the solutions of homework problems but must hand in their own solution sets separately. After the papers are collected, a solution sheet will be provided.

Final Exam (15%): This will be a take-home exam, due on the scheduled final exam day (Sa 5/8, 5pm). It will be composed of problems in the common topics similar to homework problems, but more difficult. Students must work independently on the final exam: No collaboration is allowed.


Special Topics (25% of total grade):

Homework (10%):  The instructor will assign some homework problems for each student on their special topics.

Project (15%): Each student will do a project related to their special topics, due on a day to be arranged with the instructor.


Grading: The percentage for each activity is shown in the left table below. To convert the total percentage to a letter grade, use the scale shown in the right table below.




  # total %
Common Topics Homework 8? 60
Common Topics Final Exam 1 15
Total for Common Topics 75
Special Topics Homework 2? 10
Special Topics Project 1 15
Total for Special Topics 25


Total: 100
  GP %
A 4.0 90-100
B+ 3.5 84-89
B 3.0 78-83
C+ 2.5 72-77
C 2.0 66-71
D 1.0 60-65
F 0.0 0-59



Miscellaneous policies:


If changes to this syllabus are necessary, they will be implemented after discussion and negotiation with the students.


Homework sets are due at 9:00 am on the day following the nominal due date: otherwise they are late. Any late assignments will suffer a 5% penalty per day (excluding weekends and holidays) until they are handed in: i.e., 5% on the first day, 10% on the second day...


There  will be no dropped grades. All work done in the course will be counted. There will be no extra-credit work.


The  College of Liberal Arts' academic misconduct policy will be followed. In addition, all students are bound by the Mercer University Honor Code.


Students are strongly encouraged to discuss with the instructors all their work during the course, regardless of their grades. Questions about point awards should be brought up as soon as possible, as all grades will be final one week after the materials are graded and returned to the students.


Students with a documented disability should inform the instructor at the close of the first class meeting or as soon as possible. If you are not registered with Disability Services, the instructor will refer you to the Student Support Services office for consultation regarding documentation of your disability and eligibility for accommodations under the ADA/504. In order to receive accommodations, eligible students must provide each instructor with a Faculty Accommodation Form from Disability Services. Students must return the completed and signed form to the Disability Services office on the 3rd floor of the Connell Student Center. Students with a documented disability who do not wish to use accommodations are strongly encouraged to register with Disability Services and complete a Faculty Accommodation Form each semester. For further information please contact Disability Services at 478-301-2778 or visit the website at


All requests for reasonable accommodation are welcome also in regard to absence from class for school representation (i.e., athletic or other events) or personal/family problems. Let's talk about it...