Mathematical Physics (PHYS*3130)
Code and section: PHYS*3130*01
Term: Fall 2019
Instructor: Eric Poisson
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.
Monday, Wednesday, Friday, 11:30am to 12:20pm, MacKinnon (MCKN) 231
- Wednesday October 2, in class
- Wednesday October 30, in class
Friday December 6, 8:30am. The room will be posted in due course.
Instructor: Eric Poisson
Office: MACN 452
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.
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 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.
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.
|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|
Lecture Notes (Notes)
A set of lecture notes, designed specifically for this course, is available for download on Courselink.
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.
When You Cannot Meet a Course Requirement
Undergraduate Calendar - Academic Consideration and Appeals
Graduate Calendar - Grounds for Academic Consideration
Associate Diploma Calendar - Academic Consideration, Appeals and Petitions
Undergraduate Calendar - Dropping Courses
Graduate Calendar - Registration Changes
Associate Diploma Calendar - Dropping Courses
Copies of Out-of-class Assignments
Recording of Materials
Please note: This is a preliminary web course description. The department reserves the right to change without notice any information in this description. An official course outline will be distributed in the first class of the semester and/or posted on Courselink.