Welcome to physics 466 for 2017
.
We will be using a textbook called Physical Mathematics published
by Cambridge University Press.
Insist on the 2014 printing which has many of the typos corrected.
The videos of the
lectures will be posted on YouTube:
lecture of 22 Aug
2017, sections 1.1-1.3.
lecture of 24 Aug
2017, sections 1.4-1.10.
lecture of 29 Aug
2017, sections 1.11-1.19.
lecture of 31 Aug
2017, sections 1.20-1.23.
lecture of 5 Sep
2017, sections 1.24-1.26.
lecture of 7 Sep
2017, sections 1.27-1.35. By mistake, the first half of the lecture
was not recorded.
lecture of 12 Sep
2017, sections 1.36-1.38 and 2.1.
lecture of 14 Sep
2017, sections 2.1-2.6.
lecture of 19 Sep
2017, sections 2.7-2.10.
lecture of 21 Sep
2017, sections 2.13 and 3.1-3.3.
lecture of 26 Sep
2017, sections 3.4-3.10.
lecture of 28 Sep
2017, sections 3.11-3.13 and 4.1-4.4.
lecture of 3 Oct
2017, sections 4.5-4.14.
lecture of 5 Oct
2017, sections 4.14-16 & 5.1-6
lecture of 10 Oct
2017, sections 5.6-5.12.
lecture of 17 Oct
2017, sections 5.12-5.15.
lecture of 19 Oct
2017, sections 5.15-5.19.
lecture of 24 Oct
2017, sections 5.19-5.22.
lecture of 26 Oct
2017, sections 6.1--6.4.
lecture of 31 Oct
2017, sections 6.4--6.6.
lecture of 2 Nov
2017, sections 6.7--6.14.
lecture of 7 Nov
2017, sections 6.15--6.18.
lecture of 9 Nov
2017, sections 6.18--6.22 (Principle of stationary action, homogeneous first-order ordinary differential equations, linear first-order ordinary differential equations, small oscillations, singular points of second-order ordinary differential equations, method of Frobenius, Fuch's theorem).
lecture of 14 Nov
2017, sections 6.22--6.30 (Fuch's theorem, even and odd
differential operators, Wronski's determinant, a second
solution, why not three solutions? boundary conditions, a
variational problem, formally self-adjoint differential
operators, self-adjoint differential systems, making
operators formally self adjoint).
lecture of 16 Nov
2017, sections 6.31--6.35 (making operators formally self adjoint, wronskians of self-adjoint operators,
first-order self-adjoint differential operators, a constrained variational problem, eigenfunctions and
eigenvalues of self-adjoint systems).
lecture of 21 Nov 2017:
sections 6.35--6.44 and 8.1--8.3 (completeness of
eigenfunctions of Sturm-Liouville systems, unboundedness of
eigenvalues implies completeness, delta-function example,
inequalities of Bessel and Schwarz, Green's functions,
eigenfunctions and Green's functions, Green's functions in
one dimension, principle of stationary action in field
theory, symmetries and conserved quantities, systems of
ordinary differential equations, nonlinear differential equations,
Legendre polynomials, Rodrigues's formula, generating function for Legendre's polynomials).
lecture of 28 November 2017:
sections 8.3--8.14 (generating function for Legendre's polynomials,
Legendre's differential equation, recurrence relations,
special values of Legendre's polynomials, Schlaefli's
intgeral formula, orthogonal polynomials, azimuthally
symmetric laplacian, Laplace's equation in two dimensions,
Helmholtz's equation in spherical coordinates, associated
Legendre functions, spherical harmonics, cosmic microwave
background radiation).
lecture of 30 November 2017:
sections 9.1--9.2 (Bessel functions of the first kind, spherical
Bessel functions of the first kind, quantum dots).
lecture of 5 December 2017:
sections 9.1--9.4 (Bessel functions of the first kind, wave-guides, spherical
Bessel functions of the first kind, Bessel
functions of the second kind, spherical Bessel
functions of the second kind, scattering off a hard sphere).
lecture of 7 December 2017:
sections 7.1--7.5 and 9.3--9.4 (turning differential equations into
integral equations, Fredholm equations, Volterra equations,
linearity, numerical solutions, integral transformations, Hankel
functions, Bessel functions of the second kind, spherical
bessel functions of the second kind).
ch2.pdf
Dirac on his delta function.pdf
Systems of ODEs: How to reduce a bunch
of possibly high order and possibly time-dependent ODEs to
an autonomous system of first-order ODEs and how to
numerically integrate that system in Matlab and Python.
Hamilton systems and numerically
integrating systems of differential equations (Chapter 15 of 2d edition)
Matlab codes for coupled harmonic
oscilators,
van der Pol oscillator, and Roessler system for c = 5.7
There is a list of errata
at quantum.phys.unm.edu/466-15/errata.html. Please send new errata to
me.
I started writing this book when Elsevier bought Academic Press
the publisher of the book by Arfken et al. which I had
been using. Elsevier charges so much for its journals
and books that it has made much of modern science
inaccessible to all but the wealthiest institutions and
individuals. When you start
writing papers, you should post them on an arXiv (arxiv.org and/or bioRxiv.org) and
submit them to journals not owned by Elsevier or Wiley. Pass
it on.
Here is what I plan to cover in this course:
Linear
algebra:
3 weeks
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 topics are discussed in the first nine chapters of the book.
All homework problems are stated in the book Physical Mathematics.
I will be doing some of the homework problems during
the weekly problem session which is held on Wednesdays
at 2 pm in room 5.
Put homework in Changhao Yi's mailbox by 3:00 PM on its due
date, usually a Friday.
You can send him e-mail here.
You can send me e-mail here.
Tentative list of homework assignments:
First homework assignment: Do
problems 1-14 of chapter 1 by Friday, 1 September.
Second homework assignment: Do
problems 15-28 of chapter 1 by Friday, 8 September.
Third homework assignment: Do problems 29-40 of chapter 1
by Friday, 15 September.
Fourth homework assignment: Do problems 1-14 of
chapter 2 by Friday, 22 September.
Fifth homework assignment: Do problems 15-23 of chapter 2 and
1-5 of chapter 3 by Friday, 29 September.
Sixth homework assignment: Do problems 6-18 of chapter 3 and
1 of chapter 4 by Friday, 6 October.
Seventh homework assignment: Do problems 2-18
of chapter 4 by Friday, 20 October.
Eighth homework assignment: Do problems 19-22 of chapter 4
and 1-6 of chapter 5 by Friday, 27
October.
Ninth homework assignment: Do problems 7, 10, 11, 13, 16,
17, 19, and 23 of chapter 5 by
Friday, 3 November.
Tenth homework assignment: Do problems 24-31 of chapter 5 by
Friday, 10 November.
Eleventh homework assignment: Do problems 32, 33, 36, 37,
and 38 of chapter 5 and problems 1-5 of chapter 6 by Friday, 17
November.
List of homework problems of chapter 6 with fewer
typos.
Twelfth homework assignment: Do problems 6, 8-14, and 19 of chapter 6
by Friday, 1 December.
List of homework problems of chapter 8 with some new
problems.
New version of chapter 9 with new problems.
Thirteenth homework assignment: Using the above new set of
exercises for chapter 8 and the new version of chapter 9
and its new exercises, do problems 12--15, 17,
and 18 of chapter 8 and problems 9.1, 9.13, and 9.22 of
the new chapter 9 by Friday, 8 December.
The final exam is on Thursday, 14 December
in room 184 from 5:30
to 7:30.
The Trouble with Quantum
Mechanics by Steven Weinberg. All students of physics
should read at least section 1 of this essay.