# Mathematical Physics (PHYS*3130)

Code and section: PHYS*3130*01

Term: Fall 2023

## General Information

Department of Physics
College of Engineering and Physical Sciences

PHYS*3130 (Section 01; Credit Weight 0.5) Fall 2023
Mathematical Physics

### Calendar Description

This course covers a number of mathematical techniques that are required in all areas of physics. Curvilinear coordinates, special functions, Fourier series and integral transforms, Green’s functions, and a number of advanced topics will be discussed. The course emphasizes the application of these techniques to solve a variety of physics problems, providing context to the fundamental tools of the discipline.
Pre-requisites: (1 of MATH*1160, MATH*2150, MATH*2160), MATH*2200, MATH*2270, PHYS*2310, PHYS*2340

## Course Materials

### Text

There is no single designated textbook for this course, but we will be scheduling our progress loosely following the lecture notes by Prof. E. Poisson (PDF version of which is posted on the course-link site under references), which are largely based on materials from the reference (1) in the Reference list; alternatively, for some of the topics we may select materials from (2) and (3) in the list as well. Occasionally there could be materials referenced from some additional literature materials and they will be specifically referenced in the lecture notes.

### Primary References

1. “Mathematical Methods in the Physical Sciences”, 3rd Ed. by M. L. Boas.
2. “Mathematical Methods for Students of Physics and Related Fields”, 2nd Ed. by S. Hassani.
3. “Mathematical Methods for Physicists” – A Comprehensive Guide, 7th Ed. by G.B. Arfken, H.J. Weber, and F.E. Harris.

## Course Objectives

• Acquire a working knowledge of curvilinear coordinates and how they can be involved in vector-calculus operations; illustrate Gauss’ theorem and Stokes’ theorem with emphasis on their physical interpretations.
• Illustrate various properties of special functions (including the Gamma function, Legendre polynomials, associated Legendre functions, spherical harmonics, Bessel functions, and the Dirac delta function) and their applications in solving a variety of physics problems.
• Acquire an understanding of Fourier series, Fourier transforms, and other ways of expanding functions in a basis of orthogonal functions.
• Solve the Laplace and wave equations by separation of variables, and illustrate these techniques to a range of physics problems.
• Acquire an understanding of Green’s functions in the context of Poisson’s equation and the wave equation.

## Evaluation

The choice of Schemes will favour students’ final score.

Assessments Scheme 1 Scheme 2
Participation 5% 5%
Assignments 30% 30%
Midterm Exam 30% 20%
Final Exam 35% 45%

### Assignments

The distribution dates and due dates are listed in the proposed schedule (see below). Finished work will be submitted electronically on the course-link site and the marked assignments will be released to the same course-link location. Assignment deadlines will be enforced with a late penalty of 10% per day. Once a review session in class covering content of the assignment is commenced no submission will be accepted.

## Proposed Course Delivery Schedule

Actual dates may vary and the updates will be announced on the course-link site.

Dates Contents Notes
Sept. 8 Introduction  N/A
Sept. 11, 13, 15, 18 Vector calculus and Curvilinear coordinates Assign HW#1 Sept 18
Sept. 20, 22 Gamma function N/A
Sept. 25, 27,29  Legendre polynomials HW#1 due: 11:30am, Wed Sept 27;
Assign HW#2.
Oct. 2, 4, 6, Legendre polynomials; Spherical harmonics N/A
Oct. 11,13 Spherical harmonics; Bessel functions HW#2 due: 11:30am, Wed Oct 11;
Assign EX#1 (practice questions, not due)
Oct. 16, 20 Bessel functions Midterm Exam: Oct. 18 (evening)
Oct. 23, 25, 27 Dirac delta function; Fourier series N/A
Oct. 30, Nov 1, 3 Fourier series; Expansion in orthogonal functions Assign HW#4 Nov. 3
Nov. 6, 8, 10 Fourier transform; Laplace’s equation N/A
Nov. 13, 15, 17 Laplace’s equation HW#4 due: 11:30am, Wed
Nov 15; Assign HW#5
Nov. 20, 22, 24 Wave equation N/A
Nov. 27, 29, Dec 1 Green’s function HW#5 due: 11:30am, Friday Nov. 29;
Assign EX#2 (practice questions, not due)

## Course Policies

### Getting Help

Office Hours: Tuesday 3:00 pm – 5:00 pm, (MACN 223)

Additional office hours will be arranged during the time approaching the exams, and these arrangements will be announced in class or via the course-link site.

Per request or the need of the class, we will initiate discussion areas on the course-link site associated with some selective subject (e.g. a specific assignment question or prep for an exam). You may participate to any discussion threads anomalously if you prefer.

### Collaboration versus Copying

Students are encouraged to discuss with each other during working on the problem assignments. However, the work that you submit as your assignment must not be a copy of someone else's work. Identical scripts will be given a mark of zero and plagiarism will be dealt with severely. Proper citations should be provided when books and other articles are used in your works.

### Course Assessment

The Department of Physics requires student assessment of all courses taught by the Department. These assessments provide essential feedback to faculty on their teaching by identifying both strength and possible areas of improvement. In addition, annual student assessment of teaching provides part of the information used by the Department Tenure and Promotion Committee in evaluating the faculty member’s contribution in the area of teaching. The Department’s teaching evaluation questionnaire invites student response both through numerically quantifiable data, and written student comments. In conformity with University of Guelph Faculty Policy, the Department Tenure and Promotion Committee only considers comments signed by students (choosing “I agree” in question 14). Your instructor will see all signed and unsigned comments after final grades are submitted. Written student comments may also be used in support of a nomination for internal and external teaching awards.

## University Policies

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons, please advise the course instructor in writing, with your name, id#, and e-mail contact. See the Undergraduate Calendar for information on regulations and procedures for academic consideration.

The University of Guelph is committed to upholding the highest standards of academic integrity and it is the responsibility of all members of the University community, faculty, staff, and students to be aware of what constitutes academic misconduct and to do as much as possible to prevent academic offences from occurring.

University of Guelph students have the responsibility of abiding by the University’s policy on academic misconduct regardless of their location of study; faculty, staff  and students have the responsibility of supporting an environment that discourages misconduct. Students need to remain aware that instructors have access to and the right to use electronic and other means of detection. Please note: Whether or not a student intended to commit academic misconduct is not relevant for a finding of guilt. Hurried or careless submission of assignments does not excuse students from responsibility for verifying the academic integrity of their work before submitting it. Students who are in any doubt as to whether an action on their part could be construed as an academic offence should consult with a faculty member or faculty advisor.