Mathematical Physics (PHYS*3130)

1 Course Details

1.1 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.

Prerequisites: (1 of MATH*1160, MATH*2150, MATH*2160), MATH*2200, MATH*2270, PHYS*2310, PHYS*2340

1.2 Timetable

Lectures

The course will commence in a fully remote format until Sept. 28, with the 1st in-person lecture planned for Wednesday, Sept. 29, unless changed due to public-health or University policies. It should also be noted that following Sept. 28, some scheduled in-person lectures may be moved to online format due to essential travel of the Instructor.  

1.3 Final Exam

2 Instructional Support

2.1 Instructional Support Team

 

3 Learning Resources

3.1 Required Resources

• Mathematical Methods for Students of Physics and Related Fields, by Hassani Sadri, (Springer, 2nd edition, 2009)
• Courselink (Website)

Lecture notes, links to online resources, and assignments will be posted on Courselink.

3.2 Additional Resources

At this stage of your education, you should be consulting more than one text, to enhance your learning and understanding of the material.  There are many excellent texts on mathematical techniques for physics, some more general, others providing an in-depth discussion on specific topics.  Each provides an alternative style, and may be more suitable for you. 

An alternative textbook is Essential Mathematical Methods for Physicists, by H.J. Weber and G.B. Arfkin (Elsevier Academic Press, 2004), although specific references will be made to Sadri.  

4 Teaching and Learning 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.
• Use techniques of complex analysis and apply the residue theorem to solve complex integrals.
• Demonstrate an understanding of Fourier and Laplace transforms to solve ODEs. 
• Solve the Laplace and wave equations by separation of variables, and apply these techniques to a host of physics problems.
• Expand functions and solutions to ODEs and PDEs in a basis of orthogonal functions.
• Demonstrate a working knowledge of Green’s functions in the context of one-dimensional differential equations, Laplace’s equation, and the wave equation.

5 Assessments

5.1 Marking Schemes & Distributions

The final examination has been set for Tuesday, December 7, 2021 from 19:00 - 21:00. The exam is expected to be conducted in-person; however, updates will be provided in the event that health-safety measures change in response to COVID-19.  
The midterm exam is also expected to be conducted in person, will be set in week 6 or 7, also in an evening, with a date set to minimize conflict/crowding of students’ midterm schedules.  This will be discussed in the first or second week of class.

Those students scoring less than 60% on the midterm exam may select to to write a make-up exam that would be set in week 9 or 10. The midterm exam mark would then be replaced by score on the 2nd attempt. It should not be expected that the make-up exam is easier than the 1st exam, and may also cover material given in lectures following the 1st exam. 

Assignments (8 are intended) are planned to be given on a schedule of weeks 2, 3, 4, 5 before the midterm, then weeks 8, 9, 10, 11 following the midterm, and will be due on the date of the deadline (no late assignments accepted unless prior arrangements have been made).  Completed assignments will be submitted via dropbox on Courselink.  Some questions will require computation (using python). High presentation standards are expected (legible hand writing, commented code, etc.). 

6 Course Statements

6.1 Collaboration versus Copying

Scientists work alone or in groups, very often consulting fellow scientists and discussing their research problems with peers. Collaboration is a feature of scientific activity and there are many benefits to working with others. However, no ethical scientist would ever publish or claim the work of others as his or her own and generally scientists give reference to the appropriate source of ideas or techniques which are not their own.

You are a young scientist and, in this spirit, I encourage you to discuss with others as you learn the material and work on the problem assignments. However, the work that you submit as your assignment must be your own and not a copy of someone else’s work. Identical scripts will be given a mark of zero and plagiarism will be dealt with severely. I encourage you to cite your references, citing books and other articles when they are used and acknowledging discussions with those who have helped you in your understanding and completion of the problem. This is good scientific practice.

6.2 Course Evaluation Information

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 strengths 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 Promotions Committee only considers comments signed by students. 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.

NOTE: No information will be passed on to the instructor until after the final grades have been submitted.

7 University Statements

7.1 COVID-19 Disclaimer

Please note that the ongoing COVID-19 pandemic may necessitate a revision of the format of course offerings and academic schedules. Any such changes will be announced via CourseLink and/or class email. All University-wide decisions will be posted on the COVID-19 website and circulated by email.  

Illness

The University will not normally require verification of illness (doctor's notes) for fall 2020 or winter 2021 semester courses.  However, requests for Academic Consideration may still require medical documentation as appropriate.

7.2 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.

7.3 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.  

7.4 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. Undergraduate Calendar - Dropping Courses 

7.5 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.

7.6 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.

7.7 Academic Integrity

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. Undergraduate Calendar - Academic Misconduct 

7.8 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.

7.9 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. Academic Calendars