Mathematical Physics

PHY 365 --- Fall 2003 Syllabus

Physics Department --- Mercer University

 

 Text: Mathematical Methods for Physics and Engineering, 2nd edition, 
           by K. F. Riley, M. P. Hobson, and S. J. Bence
 Class Meetings: MWF 2-2:50pm, WSC 106 
 Instructor: Dr. Jose L. Balduz Jr 
          email:  balduz_jl@mercer.edu
           phone: (478)301-2229
          office: Willet Science Center 110
          office hours: MTWRF 3-4pm
          home page:  http://physics.mercer.edu/balduz

 

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 learn some of the theory and applications, in a physics context, of the following mathematical tools: vector calculus, probability distributions, systems of linear ordinary differential equations, linear algebra and group theory as applied to coordinate transformations, Fourier analysis and orthogonal functions. 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.

 

Portions of the following chapters (and sections therein) from the text will comprise the bulk of the course, although not entirely in the textbook order: 
Ch. 8.  Matrices and Vector Spaces (all)
Ch. 9.  Normal Modes (all)
Ch. 10.  Vector Calculus (1-9)
Ch. 11.  Line, Surface, and Volume Integrals (all)
Ch. 12.  Fourier Series (all)
Ch. 13.  Integral Transforms (1)
Ch. 15.  Higher-Order Ordinary Differential Equations (1)
Ch. 17.  Eigenfunction Methods for Differential Equations (all)
Ch. 19.  Partial Differential Equations: Separation of Variables and Other Methods (1-3)
Ch. 24.  Group Theory (1-4, 6).
Note, however, that this is a large amount of material to cover in one semester; much of it will be omitted due to lack of time, even within sections listed above. In addition, some supplementary material will be provided by the instructor independent of the text:

A.  Probability Distributions
B.  Lie Groups: Rotations, Lorenz Group, Unitary Groups U(1), SU(2) and SU(3).

 

Lectures: 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.

 

Homework (60% of total grade): From each main 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.

 

Tests (2, for 40% of total grade): There will be two take-home tests, a mid-term and a final. They will be similar to homework problems, but more difficult. Students must work independently on the exams: No collaboration is allowed.

 

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 %
Homeworks ~8 60
Tests 2 40
 

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 56-65
F 0.0 0-55

 

Miscellaneous policies:

1. All parts of this syllabus are tentative and subject to revision.

2. Late homeworks and take-home tests will suffer a one-half letter grade penalty (E.g., an "A" becomes a "B+") if handed in within one week of the due date. If handed in later than that, they will suffer a full letter grade penalty. However, no credit will be given for any work handed in after the final exam due date.

3. There will be no dropped grades. All work done in the course will be counted.

4. There will be no extra-credit work.

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

6. Students are strongly encouraged to discuss with the instructor 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.

7. Students with a documented disability should inform the instructor at the close of the first class meeting. The instructor will refer you to the office of Student Support Services (SSS) for consultation regarding evaluation, documentation of your disability, and recommendations for accommodation, if needed. Students will receive from SSS the Faculty Accommodation Form. On this form SSS will identify reasonable accommodations for this class. The form must be given to the course instructor for signature and then returned to SSS.  To take full advantage of disability services, it is recommended that students contact the Office of Student Support Services, immediately. The office is located on the third floor of the Connell Student Center.

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