Physics 466, Fall 2019 Physical Mathematics

Welcome to physics 466 for 2019.

Class meets in room 184 of the physics building at 1919 Lomas NE at 5:30 pm on Tuesdays and Thursdays.
The problem session for the course, physics 468, will meet in room 5 from 5 to 5:50 and not in room 1131 as originally scheduled.

We will be using the second edition of a textbook called Physical Mathematics published this summer by Cambridge University Press.
You can get it now from Amazon and eBooks.
They are available in the UNM bookstore.

Here is Chapter 1.

Here is Chapter 2.

Here is Chapter 3.

A list of errata in the second edition of Physical Mathematics.

SYLLABUS
Here is what I plan to cover in this course:
Linear algebra:             2 weeks
Vector calculus              0.5
Fourier series:                1.5
Fourier transforms:        1.5
Infinite series:               1
Complex variables:       3
Differential equations:  3
Integral equations:        0.5
Legendre polynomials:  1.5
Bessel functions:            1.5
These are the first ten chapters of the book.

All homework problems are stated in the book Physical Mathematics. Put homework in Evgeni Zlatanov's mailbox by 3:00 PM on its due date, usually a Friday. You can send him e-mail here.
I will be doing some of the homework problems during the weekly problem sessions which are held on Wednesdays at 5 pm in room 5.
You can send me e-mail here.

Homework 1 due Friday 30 August:
Do problems 1-3, 5-7, & 9-14 of chapter 1.
Homework 2 due Friday 6 September:
Do problems 15-22, 25, 27-31 of chapter 1.
Homework 3 due Tuesday 17 September:
Do problems 1.32-1.36 and 1.40 and 2.2-2.6 of chapter 2.
Homework 4 due Friday 27 September:
Do problems 3.1, 3.2, 3.4-3.12, and 3.16-3.21 of chapter 3.

Videos of lectures:
20 August
Linear algebra: Sections 1.1 Numbers, 1.2 Arrays, 1.3 Matrices, 1.4 Vectors, 1.5 Linear operators, 1.6 Inner products, 1.7 Cauchy–Schwarz inequalities, and 1.8 Linear independence and completeness.
22 August
1.9 Dimension of a vector space, 1.10 Orthonormal vectors, 1.11 Outer products, 1.12 Dirac notation, 1.13 Adjoints of operators, 1.14 Self-adjoint or hermitian linear operators, 1.15 Real, symmetric linear operators.
27 August
1.16 Unitary operators, 1.17 Hilbert spaces, 1.18 Antiunitary and antilinear operators, 1.19 Symmetry in quantum mechanics, 1.20 Determinants, 1.21 Jacobians, 1.22 Systems of linear equations, 1.23 Linear least squares, and 1.24 Lagrange multipliers.
29 August
1.24 Lagrange multipliers, 1.25 Eigenvectors and eigenvalues, 1.26 Eigenvectors of a square matrix, 1.27 A matrix obeys its characteristic equation, 1.28 Functions of matrices, and. 1.29 Hermitian matrices.
3 September
1.30 Normal matrices, 1.31 Compatible normal matrices, 1.32 Singular-value decompositions, 1.33 Moore-Penrose pseudoinverses, 1.34 Tensor products and entanglement, 1.35 Density operators, 1.36 Schmidt decomposition, 1.37 Correlation functions, 1.38 Rank of a matrix, and 1.39 Software.
5 September
2.1 Derivatives and partial derivatives, 2.2 Gradient, 2.3 Divergence, 2.4 Laplacian, and 2.5 Curl
10 September
3.1 Fourier series, 3.2 The interval, 3.3 Where to put the 2pi’s, 3.4 Real Fourier series for real functions, 3.5 Stretched intervals, 3.6 Fourier series of functions of several variables, 3.7 Integration and differentiation of Fourier series, and 3.8 How Fourier series converge.
12 September
3.9 Measure and Lebesgue integration, 3.10 Quantum-mechanical examples, 3.11 Dirac’s delta function, 3.12 Harmonic oscillators, 3.13 Nonrelativistic strings, and 3.14 Periodic boundary conditions.


All students of physics should read at least the first section of the essay The Trouble with Quantum Mechanics by Steven Weinberg before they graduate.