Physics 228

Mathematical Methods of Physics (II)

Autumn 2009
Instructor: Laurence G. Yaffe
Office: PAB 404
Office hours: Mondays, 2-4 and Fridays 3:45-5
TA: Gary Howell (PAB 427, gthowell@hotmail.com)
Class meetings: 9:30-10:20pm MWThF, PAB 109
Course website: http://courses.washington.edu/phys2278/
Syllabus
Grading
Textbook
Notes
Homework
Cornu spiral

Overview

    This course is a continuation of Phys 227, and is devoted to basic mathematical methods of physics. Topics covered include ordinary differential equations, Fourier series and integrals, calculus of variations, useful special functions such as Legendre polynomials and Bessel functions, and basic partial differential equations.
1d wave equation

Course objectives

    Acquire practical facility with the mathematical methods covered, and experience in applying these methods to common physics applications such as forced and coupled oscillators, electrostatics, wave equations, diffusion and Schrodinger equations.
Damped oscillator

Grading

    There will be weekly homework assignments, weekly quizzes, and a final exam. Discussing homework problems in groups is encouraged, but you must write up your own solutions. Assignments and solutions will be posted on the class website. Weekly quizzes will feature material covered in previous homework assignments. Grades will be based approximately 40% on quizzes, 20% on homework, and 40% on the final.

Final Exam

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Lorenz attractor

Prerequisite

    Phys 227 (Math Methods I).

Mathematica

    Use of a computer mathematics program such as Mathematica is an integral part of this course. Mathematica is available on all the physics PCs in B101, and on all the machines in the AM018 study center (under the physics lecture halls). Students may purchase the Mathematica student version from the University Book Store at a discounted price. Brief instructions on getting started may be found in this Mathematica primer. Also useful is this Hands-On Introduction to Mathematica which is best viewed while running the demo within Mathematica.
1d Wave packet

Textbook

    Mathematical Methods in the Physical Sciences (3rd ed) by Mary L. Boas. Corrections to the text are available here. Note that solutions to some problems appear at the back of the book (and there is a companion volume to the previous edition which contains solutions to approximately 1/4 of the exercises, many of which are the unchanged in the current edition).
    Lectures will include some material not covered in the text!
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Circular drum vibrations

Tentative syllabus

    Dates Topic Boas Chapter Lecture Notes
    Sep 30 - Oct 5 Ordinary differential equations
      Integrating factors and separation of variables. Constant coefficient linear differential equations. Applications to mechanical and electrical physical systems.
    		814
    Oct 7 - Oct 9 Fourier series
      Periodically driven systems. Orthogonal basis sets in function space. Dirac delta function.
    		715
    Oct 12 - Oct 15 Fourier transforms
      Limit of infinite period. Continuous sets of basis functions.
    		716
    Oct 16 - Oct 22 Analytic functions
      Analyticity. Residues. Cauchy residue theorem. Evaluation of integrals in the complex plane.
    		1417
    Oct 23 - Oct 28 Laplace transforms
      Inhomogeneous 2nd order ODEs with general (non-integral) driving terms. Inverting Laplace transforms.
    		8 & 1418
    Oct 29 - Nov 2 Green's functions
      More on inhomogeneous 2nd order ODEs with general driving terms.
    		8 & 1419
    Nov 4 - Nov 9 Calculus of variations
      Hamilton's principle, Lagrangian formulation of classical mechanics.
    		920
    Nov 11Veteran's Day Holiday
    Nov 12 - Nov 18 Legendre polynomials I
      Laplace equation in spherical coordinates, series solutions of ordinary differential equations.
    		1221
    Nov 19 - Nov 25 Legendre polynomials II
      orthogonality & completeness, normalization, expansions in Legendre polynomials, associated Legendre functions, spherical harmonics
    		1222
    Nov 26 - Nov 27Thanksgiving Holiday
    Nov 30 - Dec 3 Frobenius and Bessel
      Method of Frobenius, Laplace equation in cylindrical coordinates, Bessel functions.
    		1223
    Dec 4 - Dec 7 Partial differential equations I
      Homogeneous, time-independent linear PDEs, Laplace and Helmholtz boundary value problems.
    		1324
    Dec 9 - Dec 11 Partial differential equations II
      Time dependent & inhomogeneous linear PDEs, Poisson equation.
    		1325 & 26
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CMB spectrum

Lecture Notes

The following lecture notes, prepared by Prof. Steve Ellis, are a primary reference for the course. Study them carefully! The sample problems show solutions to selected textbook problems illustrating the material in each chapter of notes. Also available are Mathematica notebooks illustrating the solution of problems covered in the lecture notes and in the sample problems. 		Top
Heat equation

Homework Assignments

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