MA/PH 607
Howell
9/14/2011
Homework Handout IV
A. Let
U
"
&
#
'
#3
$!
#
&
"
'
3
$!
!
"
'
&3
$!
.
1. Compute UT and U .
2. Verify that U is unitary.
3. Let U e e" e# e$ f be any orthonormal set of vec
MA/PH 607
Howell
9/14/2011
Homework Handout IV
A. Let
U
"
&
#
'
#3
$!
#
&
"
'
3
$!
!
"
'
&3
$!
.
1. Compute UT and U .
2. Verify that U is unitary.
3. Let U e e" e# e$ f be any orthonormal set of vec
2
Traditional Vector Theory
The earliest denition of a vector usually encountered is that a vector is a thing possessing
length and direction This is the arrow in space view with length naturally bein
Three Coordinate Sytems for the Plane
(Each with a Cartesian System)
1. Relative to the e B C f system, the
curves ? ?! and @ @! are
straight lines with slopes
"
and 2,
$
respectively. The ? ?! curve
Preparing for Test II
The test covers everything from Elementary Linear Transform Theory up through
Wednesdays discussion of curves and derivatives (In the online notes: chapters 6, 7
and pages 1 to t
MA/PH 607
10/14/2011
Howell
TAKE HOME PORTION OF
TEST II
(40 points)
GENERAL NOTES:
Due at the beginning of class on Friday, October 21.
This is NOT to be a team effort. Do your own work! (You may, of
MA/PH 607
10/14/2011
Howell
TAKE HOME PORTION OF
TEST II
(40 points)
GENERAL NOTES:
Due at the beginning of class on Friday, October 21.
This is NOT to be a team effort. Do your own work! (You may, of
Preparing for the First Exam
The test covers everything done up through change of bases" and volumes of hyperparallelepipeds" (Chapter 5 in the online notes). The problems will be more
computational t
The Sheet That Should Be Handed Out
The First Day Of Class
Mathematical Methods for Physicists ~ Fall 2011
(revised 8/18/2011)
General Stuff
Course: Mathematical Methods (for Physicists), MA 607 and P
Note on Example 1.8.3
(page 46 of A&W)
I've done enough partial derivation of equation 1.80 to believe it is true. However,
their derivation is garbage. In using the BACCAB rule they seem to ignore th
Multidimensional Calculus: Differential Theory
9.5
Chapter & Page: 919
General Formulas for the Divergence and Curl
Later, we will discover the geometric signicance of the divergence and the curl of a
Multidimensional Calculus: Differential Theory
9.3
Chapter & Page: 913
The Classic Gradient, Divergence and Curl
Basic Denitions in Euclidean Space
For expediency, we will rst dene the classical diffe
Multidimensional Calculus: Differential Theory
Chapter & Page: 99
Final Comments on Christoffel Symbols and Acceleration
Using the above, we can nd formulas for acceleration (and Christoffel symbols)
9
Multidimensional Calculus:
Mainly Differential Theory
In the following, we will attempt to quickly develop the basic differential theory of calculus in
multidimensional spaces. Youve probably alread
9
Multidimensional Calculus:
Mainly Differential Theory
In the following, we will attempt to quickly develop the basic differential theory of calculus in
multidimensional spaces. Youve probably alread
8
Multidimensional Calculus: Basics
Weve nished the basic linear algebra part of the course; now we start a major part on
multidimensional calculus This will included discussions of eld theory, differ
1
Intro
1.1
Some of What We Will Cover
Here is a very rough idea of what the rst part of the Math Physics course will cover:
1.
Linear Algebra
(a) We will start with a fundamental development of the t
MA/PH 607
Howell
11/7/2011
Homework Handout IX
A. For the following problems, we will use Cartesian
coordinates to describe points in the plane, and will
let V" , V# , V$ and V% be the four curves fro
MA/PH 607
Howell
10/31/2011
Homework Handout VIII
A. In a previous problem, you sketched the curves
x>
3> 9>
> #1 >
with
x>
3> 9>
>#
with
x>
3> 9>
% >
1
$
0>
>
with 0 > 41
Now:
.x
in terms of the
MA\PH 607
Howell
10/18/2011
Homework Handout VII
Addendum
(version 1)
A. Let e ? @ f be a basis-based coordinate system for the plane based on a basis e b" b# f
as indicated below. Assume the smallest
MA\PH 607
Howell
10/14/2011
Homework Handout VII
A. Two e ? @ f coordinate systems for the plane are sketched below. On each, plot the points
! ! , " # and
" # . Also, sketch the curve (well as you ca
MA/PH 607
Howell
10/3/2011
Homework Handout VI
A. The following all involve linear operators on a two-dimensional traditional vector space i
with standard basis U e i j f. Try to do all of these probl
MA/PH 607
09/23/2011
Homework Handout V
A. Let i be a two-dimensional traditional vector space with standard basis T e i j f .
Using this basis for i , do the following (unless otherwise indicated, vi
MA/PH 607
Howell
9/14/2011
Homework Handout IV
A. Let
U
"
&
#
'
#3
$!
#
&
"
'
3
$!
!
"
'
&3
$!
.
1. Compute UT and U .
2. Verify that U is unitary.
3. Let U e e" e# e$ f be any orthonormal set of vec
MA/PH 607
9/9/2011
Homework Handout III
A. Read 4.1 in the online notes, doing any in-notes exercises.
Also skim/read 3.2 of A&W (Arfken & Weber), starting with Basic Definitions at the
bottom of page
MA/PH 607
8/29/11
Homework Handout II
A. For the following, i is a three-dimensional space of traditional vectors with standard basis
f ei jkf
(If you prefer, use e e1 e2 e3 f or e x y z f .)
Also, le
MA/PH 607
8/17/2011
Homework Handout I
Note: In skimming/reading the indicated sections of A&W (Arfken and Weber) keep in mind
that their basic approach to the traditional vector theory is quite diffe
3
General Vector Spaces
Much of what we did with traditional vectors can also be done with other sets of things We
.
will develop the appropriate theory here, and extend our notation appropriately.
On