Mathematical Methods of Physics --- 466.001
       Monday and Wednesday from 5:30 till 6:45 pm in room 184.

       Here is the current version of the class notes.  I often update these notes, so you might want to print out just what you need rather than the whole 350 pages.  For those with sharp eyes who want to save paper, here are the notes in a smaller font.
       The class notes now have an index to the first few chapters.

       The grader is Travis McIntyre (tpm@unm.edu).

       No textbook is required for this course, but there are some decent ones:
       Mathematical Methods for Physics and Engineering by K. F. Riley, M. P. Hobson, and S. J. Bence (Cambridge Univ. Press),
       A Guided Tour of Mathematical Methods for the Physical Sciences by Roel Snieder (Cambridge Univ. Press), and
       MATHEMATICAL METHODS FOR PHYSICISTS (Academic Press) by Arfken; I prefer the later printings of the third edition.

       First homework assignment:  Do the first eight problems at the end of chapter 1 of the on-line notes.  This assignment is due on 17 September.  Solutions.
       Second homework assignment:  Do problem 1.9 and all five problems of chapter 3.  This assignment is due on Wednesday, 8 October.  Solutions.
       Third homework assignment:  Do all the problems at the end of chapter 4 by Monday, 27 October.  Solutions.
       Fourth homework assignment:  Do all the problems at the ends of chapters 5 and 6 by Wednesday 19 November.  Solutions to the problems of chapters 5 and 6.
       Fifth homework assignment:  Do all the problems at the end of chapter 8 by Monday, 1 December.
       Sixth homework assignment:  Do all the problems at the end of chapter 9 as well as the last two problems of chapter 2 by the afternoon of the final exam, which will be a lecture.  I will add some problems on the material of chapter 7.

       Videos of lectures (these wmv files are big, so please download each one to your computer before viewing it):
       First lecture: linear algebra up to linear independence.
       Second lecture:  Dirac notation and determinants.
       Third lecture:  eigenvectors and eigenvalues.
       Fourth lecture:  hermitian and normal matrices, a matrix satisfies its characteristic equation.
       Fifth lecture:  the singular-value decomposition.
       Sixth lecture:  SVD examples, tensor products, density operators, Fourier series.
       Seventh lecture:  real and complex Fourier series on various intervals, examples.
       Eighth lecture:  convergence and continuity of Fourier series, quantum-mechanical examples.
       Ninth lecture:  non-relativistic strings, periodic boundary conditions, Fourier transforms, gaussians, derivatives of Fourier transforms.
       Tenth lecture:  the diffusion equation and Fourier's solution, position and momentum space in quantum mechanics.
       Eleventh lecture:  convolutions and why they occur so often in physics.
       The twelfth lecture on convolutions , Green's functions, and infinite series is unavailable because the hard disk of the laptop failed.
       Thirteenth lecture:  power, binomial, logarithmic, and asymptotic series; analytic functions, Cauchy's integral theorem.
       Fourteenth lecture:  Cauchy's integral formula, the Cauchy-Riemann conditions, alternative proof of Cauchy's integral theorem, harmonic functions, Taylor series.
       Fifteenth lecture:  Cauchy's inequality, Liouville's theorem, the fundamental theorem of algebra, Laurent series.
       Sixteenth lecture:  calculus of residues, examples of contour integration.
       Seventeenth lecture:  logarithms and cuts, examples of contour integration, Cauchy's principal value and related delta-function identities.
       Eighteenth lecture:  The Feynman propagator for neutral scalar fields, dispersion relations, Hilbert transforms.
       Nineteenth lecture:  Kramers-Kronig relations, conformal mapping, the method of steepest descent, applications to string theory; basic facts about ordinary and partial differential equations, separability of the laplacian in various coordinate systems.
       Twentieth lecture:  Wave equations and some of their solutions, fields of different spins as solutions of wave equations, exact and separable first-order differential equations, integrating factors, examples, homogeneous functions.
       Twenty-first lecture:  The virial theorem, the general solution to a first-order linear differential equation, examples, singular points of second-order ordinary differential equations.
       Twenty-second lecture:  Hidden separability, exactness and integrability, relation to the Cauchy-Riemann conditions, homogeneous first-order ODEs, power-series method of Frobenius, even and odd differential operators, parity, Fuch's theorem, Wronski's determinant, examples.
       Twenty-third lecture:  The use of the wronskian to find a second solution, why there aren't three solutions to a second-order linear, homogeneous ODE, the self-adjoint form of a second-order linear, homogeneous ODE, boundary conditions.
       Twenty-fourth lecture:  Eigenfunctions and eigenvalues, the inequalities of Bessel and Schwarz,  Green's functions.
       Twenty-fifth lecture:  Green's function for an ODE, Legendre polynomials, recurrence relations, orthogonality, associated Legendre polynomials, spherical harmonics, covariant and contravariant vectors.
       The twenty-sixth lecture was not recorded because a volunteer camera-man forgot to click on the record icon.  The subjects covered were:  covariant and contravariant vectors and fields,  euclidean and Minkowski spaces, special relativity, time dilation.
       Twenty-seventh lecture:  special relativity: kinematics, dynamics, and electrodynamics.
       Lecture of 1 Dec 08:  special relativity, electrodynamics, tensors, adding tensors, tensor equations, summation convention, contractions, symmetry of tensors, products of tensors, the quotient rule, the metric tensor, the sphere, the contravariant metric tensor, orthogonal coordinates in flat 3-space, cylindrical and spherical coordinates, the gradient of a scalar field, derivatives and affine connections.
       Lecture of 3 Dec 08:  covariant derivatives, covariant derivatives and antisymmetry, affine connections and the metric tensor, covariant derivative of the metric tensor, divergence of a contravariant vector, the covariant laplacian, generally covariant equation of motion for a charged particle in a gravitational and an electromagnetic field, gravitational fields that are weak and static.