Files and Resources for Math Methods (TECP TTVN)
Here are the notes:
2007-03-26 Most of the following are scanned examples and notes.
They are PNG files, which should open in any recent browser. They are
scanned at 300 dpi, scaling has been a bit of a problem but if you
use a print preview and scale to about 25 percent, they should fit
on a page:
On Wed. 2007-03-28 I plan to overview the way more general
complex functions are defined, a topic not touched on in the book.
Here is a draft of an article about that: Complex
functions and multifunctions. This has been updated Wed. morning
with more figures.
- 07-01-19: Scaling and the Trinity Explosion
- 07-01-22: Homework
- 07-01-22: Lift Coefficient
- 07-01-24: Taylor Series
- 07-01-26: Dealing with small variations
- 07-01-29: Layers and multiple reflections
Also includes Homework Assignment 2.
- 07-01-31: Spherical and cylindrical coords 1
- 07-02-02: Spherical and cylindrical coords 2
- 07-02-05: Gradient 1
Includes introduction to path integral and directional derivative.
- 07-02-05: Newton's Second Law from a potential
- 07-02-07: Total derivative, continuous systems
Includes Homework assignment 3.
Here is a link to the Java demo applets for
- 07-02-09: Introduction to divergence.
- 07-02-12: Stability of orbits in higher dimensions.
Revised since presentation.
It turns out the gradient is really a tensor, a 1-form. I am working on a
Draft on tensors if you want to look at it.
- 07-02-14: Useful derivation from 6.2 for 6.5,
review of cross product for next chapter.Updated since class
- 07-02-16: Curl, vorticity.
- 07-02-19: Theorem of Gauss.
- 07-02-19: Test 1: Due Tuesday, Feb 27.
- 07-02-21: Pre-class draft: Section 8.3,
Acoustic representation theorem. This is in "article" rather
than "slide" form, better for printing. Shows many of the steps in
the section more explicitly.Slightly revised Wed. morning
- 07-02-21: Slides on 8.3: acoustic
representation to go with above. Has different commentary, so
look at both of these and the text to understand what is going on.
- 07-02-23: Flow of probability. An
application of Gauss's law to quantum mechanics
- 07-02-26: Theorem of Stokes.
with some applications to Maxwell's equations.
- 07-02-28: Wingtip vortices.
How do airplanes fly?
- 07-03-02: Ch 10: Curvature.
Introduction to ch. 10. These notes are short, I will elaborate in
class. Includes next homework assignment.
- 07-03-05: Ch 10: Shortest distance
between two points. These are the notes I went over in class on paper
Your text uses the same procedure extended to a two-dimensional soap film
to introduce the Laplacian in section 10.3. However, I have made another:
- 07-03-05: Intro to Laplace's equation
and harmonic functions.
- 07-03-07: Some properties of
the Laplacian, average of a harmonic function.
- '07-03-09 (Friday) Since we discussed doing the class differently, I will mainly try
homework help on the last assignment today. Our next chapter will
be on analytic functions: Ch. 16. Over or at the end of break
I will post some article-form help about complex variables and
example problems. See the next note:
- My jury duty was cancelled.
We started discussing chapter 16: Analytic functions
- 2007-03-19 You should work through section 16.1 problems b-e.
None of these have difficult steps, in particular
b and c are easy: just writing out the differential coefficient and
taking the given limits gives you the Cauchy-Riemann equations.
- 2007-03-23 We started covering Ch. 17, up through section 17.3
on calculating integrals with the residue theorem. Since the text only
does a few examples without much background, there is more below:
Homework for residues: 070328_HW.pdf
I originally had this due Friday, Apr. 6, but I forgot that Easter was
this close, so it is due Monday, Apr. 9, since there probably won't
be anyone here Friday either. The problems are fairly short and just like
the examples, so you can probably get it done early.
Here is a single-sheet: Basic terminology and
formulas for complex variables (PDF).
'07-04-02 (Monday)We started on Ch. 15 -- Fourier analysis,
covering section 15.1. We also talked about analogies with finite
The fourier series applet is
'07-04-04 (Wednesday)We will briefly continue talking about
vector and function spaces and the complex form of Fourier series.
We will also go over some concepts and
properties of the Dirac delta function.
Chapter 14 covers this in detail but we mainly just want results,
in particular equations 14.11,17,20,24, and 31.
There is an uncorrected error in Ch. 14: on page 206, bottom
paragraph under problem a, the sentence should be: 'This expression
states that the "surface area" under the delta frequence is one.'
Here is Test 2, due Tuesday,
'07-04-13: Here is some info on
Fourier transform conventions for the most common systems, with
some pointers to resources on the web. This is a work in progress,
covering differences between the various locations of pi, etc.
The Final Exam is here. It is due
Wednesday, May 2.
The Errata page for
Math formulary (PDF)
Physics formulary (PDF)
These are free formula compendia off of the web. The original address is
in the introduction to each file. I will probably replace
them with links to the original site soon.
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