Physics 475: Introduction to Mathematical Physics
Revised, Spring 2003. This course is cross listed as APSC 446.
Vital Information for Phys 475
Text Mary Boas: Mathematical Methods in the Physical Sciences, 2nd Ed., Wiley. Instructor Mike Finn, Room 331, Small Hall, x1-3514. finn@physics.wm.edu Grader Rui Yang, Room 318B, Small Hall x1-3550, rxyang@mail.wm.edu Meeting times Lecture: TR 12:30 PM 1:50 PM SMALL HALL ROOM 102. Objectives
The course is geared towards teaching general methods of solving partial differential equations in the physical sciences, with examples taken from common second-order secular equations. Time independent Laplace and Poisson equations, and time-dependent wave, diffusion and Schrödinger equations are featured. Similarity in methodology across physical disciplines is emphasized, with examples taken from electromagnetism, gravity, waves in membranes and on bulk media, thermodynamics, and quantum mechanics.
This course is recommended for students planning to continue on in graduate study in physics or a related scientific or engineering specialization, however, it assumes a relatively low level of knowledge, appropriate to junior/senior physics majors, and avoids unnecessary formalism. The goal will be to cover as much ground as possible. The text by Boas is clear and easy to follow. Supplementary advanced material from graduate texts will be introduced as needed.
After covering preliminary material on infinite series, complex analysis, and special functions, series solutions to differential equations are developed in detail, using Strum-Liouville Theory. Then partial differential equations are solved, via separation of variables in various coordinate systems, with emphasis on boundary value techniques. Integral approaches, such as Green functions and propagators are then covered.
In Class Problem Presentations
Passive knowledge is worthless. Active participation is intended to be a major component of the course. A percentage of your grade will be based on oral presentation of homework problems. Because of the difficulty in scheduling a separate problem session in the past, this year I plan on setting aside time during lecture for these presentations. Each student will present 2 problems over the course of the semester. You will be graded primarily on content and correctness of the written solutions, but helpful critiques will be made to improve your ability to communicate physical ideas in a clear and concise manner. The group interactions should be fun.
Outline of Topics to be Covered
- Chapter 1: Convergence of Series
- Chapter 2: Complex Functions
- Chapter 7: Fourier Series
- Chapter 11: Special Functions
- Chapter 12: Series Solutions of Differential Equations
- Chapter 13: Partial Differential Equations
- Chapter 15: Integral Transforms
Grading Policy
Grade will be based on the following distribution:
In Class Presentations 10% Homework 20% Test 1 20% Test 2 20% Final 30% 93% or better is an A. Other letter grades will be based on a curve as needed.
Preliminary Schedule
(Preliminary Schedule by Week: Due dates to be determined)
Week Assignment Due Problem Assignments 1 No homework Short week: First class meeting, orientation and lecture 2 Homework # 1 Boas Chapter 1::Infinite Series: 1.12, 4.5, 6.15, 9.15, 10.20, 13.20, 14.3, 15.3, 15.28, 15.30 3 Homework # 2 Boas, Chapter 2::Complex Numbers: 5.68, 6.14, 10.9, 11.17, 12.20, 12.36, 14.18, 17.22, 17.29 4 Homework # 3 Boas, Chapter 7::Fourier Series: 4.13, 5.1, 6.12, 9.15, 9.23, 11.2, 11.5 5 Homework # 4 Boas, Chapter 11::Special Functions: 3.14, 5.2, 7.3, 10.8, 13.14, 12.16, 12.18 6 Test 1 Covers Chapters 1, 2, 7, 11 7 Homework # 5 Boas Chapter 12::Series Solutions to Differential Equations: 1.18, 2.1, 3.6, 5.4, 5.10, 6.6, 7.2 8 Spring Break 9 Homework # 6 Boas Chapter 12::Series Solutions to Differential Equations: 9.1, 9.16, 10.2, 11.5, 12.1, 12.4, 13.5 10 Homework # 7 Boas Chapter 12::Series Solutions to Differential Equations: 15.2, 15.8, 16.3, 17.4, 17.6, 19.2, 21.17 11 Test 2 Covers Chapter 12 12 Homework # 8 Boas Chapter 13::Partial Differential Equations: 1.3, 1.4, 2.4, 2.5, 3.8, 4.5, 5.2, 5.8 13 Homework # 9 Boas Chapter 13::Partial Differential Equations: 6.2, 6.3, 6.5, 7.7, 7.11, 7.14, 8.1 14 Homework # 10 Boas Chapter 15::Integral Transforms: 2.1, 2.19, 3.2, 3.43, 4.2, 8.1, 8.8 15 No Homework Final week of classes before exams