# Mathematical Physics (PHYS*3130)

Code and section: PHYS*3130*01

Term: Fall 2019

Instructor: Eric Poisson

## Course 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.

## Timetable

### Lectures

Monday, Wednesday, Friday, 11:30am to 12:20pm, MacKinnon (MCKN) 231

### Midterm exams

• Wednesday October 2, in class
• Wednesday October 30, in class

### Final Exam

Friday December 6, 8:30am. The room will be posted in due course.

## Instructional Support

Instructor: Eric Poisson
Email: epoisson@uoguelph.ca
Extension: 53653
Office: MACN 452

## Course Objectives

By the end of this course, you should be able to:

• Demonstrate a working knowledge of curvilinear coordinates and how they can be involved in vector-calculus operations.
• Apply special functions (including the Gamma function, Legendre polynomials, spherical harmonics, Bessel functions, and the Dirac delta function) to solve a variety of physics problems.
• Demonstrate 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 apply these techniques to a host of physics problems.
• Demonstrate a working knowledge of Green’s functions in the context of one- dimensional differential equations, Laplace’s equation, and the wave equation.

## Evaluation

The final mark for the course will be the highest of the two marks calculated under the following two schemes. No other marking schemes will be considered.

Scheme Assignments Midterm 1 Midterm 2 Final Exam
A 20% 20% 20% 40%
B 20% 15% 15% 50%

A set of homework assignments will be made available on Courselink, to be returned in class by the assigned due date. The deadline will be enforced strictly, and a  penalty will be applied to late assignments. Special arrangements for late  submission must be made well ahead of time. No partial credit will be given to unaccepted assignments. Assignments provide 20% of the course’s final mark.

In marking scheme A, the two midterm exams account for 40% of the final mark (20% each), and the final exam also accounts for 40%. In marking scheme B, the midterms account for 30% of the final mark (15% each), while the final exam accounts for 50%.

Midterm and final exams will be closed-book exams, meaning that you will not be allowed to consult your notes nor any other source of information. You will, however, be provided with relevant information and a formula sheet. Calculators may be required; only non-programmable pocket calculators are permitted.

Personal communication or entertainment devices (such as smart phones or MP3 players) are not permitted during the exams.

## Proposed Schedule

The following table provides a rough guide of the material covered during each week of the semester, as well as key information regarding assignments and midterm exams. All dates are tentative; check Courselink regularly to get the most updated information. Regular attendance at lectures and tutorials is the best way to ensure that you are up to date on the relevant course material.

Week Material Covered Activity
Sept 6 Introduction
Sept 9, 11, 13 Curvilinear coordinates
Sept 16, 18, 20 Gamma function; Legendre polynomials
Sept 23, 24, 27 Legendre polynomials Assign. #1 due: 11:30am, Wed Sept 25
Sept 30, Oct 2, 4 Spherical harmonics Midterm #1: in class, Wed Oct 2
Oct 7, 9, 11 Bessel functions
Oct 16, 18 Bessel functions; Dirac delta function Assign. #2 due: 11:30am, Wed Oct 16
Oct 21, 23, 25 Dirac delta function; Fourier series
Oct 28, 30, Nov 1 Expansion in orthogonal functions Midterm #2: in class, Wed Oct 30
Nov 4, 6, 8 Fourier transforms; Laplace equation Assign. #3 due: 11:30am, Wed Nov 6
Nov 11, 13, 15 Laplace equation
Nov 18, 20, 22 Wave equation
Nov 25, 27, 29 Green’s functions Assign. #4 due: 11:30, Wed Nov 27

## Learning Resources

### Required Resources

Lecture Notes (Notes)

### Recommended Resources

Mathematical Methods in the Physical Sciences (Textbook)
Mary L. Boas, Mathematical Methods in the Physical Sciences, Third edition (Wiley, 2005)

The book by Boas contains excellent presentations of most of the topics covered in class, at just the right level for this course.

Mathematical Methods for Physicists (Textbook)
G.B. Arfken, H.J. Weber, F.E. Harris, Mathematical Methods for Physicists, 7th edition (Elsevier, 2012)

For a longer term, encyclopedic reference, the book by Arfken, Weber, and Harris is an excellent companion.

## University Statements

### Email Communication

As per university regulations, all students are required to check their e-mail account regularly: e-mail is the official route of communication between the University and its students.

### When You Cannot Meet a Course Requirement

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons please advise the course instructor (or designated person, such as a teaching assistant) in writing, with your name, id#, and e-mail contact. The grounds for Academic Consideration are detailed in the Undergraduate and Graduate Calendars.

### Drop Date

Students will have until the last day of classes to drop courses without academic penalty. The deadline to drop two-semester courses will be the last day of classes in the second semester. This applies to all students (undergraduate, graduate and diploma) except for Doctor of Veterinary Medicine and Associate Diploma in Veterinary Technology (conventional and alternative delivery) students. The regulations and procedures for course registration are available in their respective Academic Calendars.

### Copies of Out-of-class Assignments

Keep paper and/or other reliable back-up copies of all out-of-class assignments: you may be asked to resubmit work at any time.

### Accessibility

The University promotes the full participation of students who experience disabilities in their academic programs. To that end, the provision of academic accommodation is a shared responsibility between the University and the student.

When accommodations are needed, the student is required to first register with Student Accessibility Services (SAS). Documentation to substantiate the existence of a disability is required; however, interim accommodations may be possible while that process is underway.

Accommodations are available for both permanent and temporary disabilities. It should be noted that common illnesses such as a cold or the flu do not constitute a disability.

Use of the SAS Exam Centre requires students to book their exams at least 7 days in advance and not later than the 40th Class Day.

For Guelph students, information can be found on the SAS website

For Ridgetown students, information can be found on the Ridgetown SAS website

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 encourages academic integrity. 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.

### Recording of Materials

Presentations that are made in relation to course work - including lectures - cannot be recorded or copied without the permission of the presenter, whether the instructor, a student, or guest lecturer. Material recorded with permission is restricted to use for that course unless further permission is granted.

### Resources

The Academic Calendars are the source of information about the University of Guelph’s procedures, policies, and regulations that apply to undergraduate, graduate, and diploma programs.