Math 157b. Spring 2005.
Homework problems
1. Let M be a complete simply connected Riemannian manifold of constant sectional curvature.
(a) Show that the isometry group of M acts transitively on the set
cfw_(x, y) M M : d(x, y) = r.
(b) Prove that
Isom(S n
Course Notes
Solving the Schrdinger Equation: Resolvents
o
051117 F. Porter
Revision 111109 F. Porter
1
Introduction
Once a system is well-specied, the problem posed in non-relativistic quantum mechanics is to solve the Schrdinger equation. Once the solut
Physics 129a
Problem Set Number 9
Due Friday, December 7, 2012
Reading: Finish reading the course note on the calculus of variations.
Chien-Yao Tseng will grade this assignment.
35. NOTE: This problem was deferred from problem set 8.
The Legendre polynomi
Physics 129a
Problem Set Number 8
Due Friday, November 30, 2012
Reading: Finish reading the course note on Solving the Schrdinger Equao
tion: Resolvents. Read the rst two sections of the course note on the
Calculus of Variations.
Chien-Yao Tseng will grad
Physics 129a
Problem Set Number 7
Due Monday, November 26, 2012
Reading: Finish reading the course note on Linear Dierential Equations
(that is, read section 7). Also, we will conclude our discussion of Green
functions by returning to the subject of resol
116
Frank Porter
February 26, 2013
Chapter 6
Hypothesis Tests
Often, we want to address questions such as whether the possible observation
of a new eect is really signicant, or merely a chance uctuation. Also, we
frequently ask whether a given model provi
Goodness-of-Fit Considerations and Comparisons
Case Study: Testing Consistency of Two Histograms
Sometimes we have two histograms and are faced with the question:
Are they consistent?
That is, are our two histograms consistent with having been sampled
fro
Frank Porter
March 1, 2011
Chapter 7
Density Estimation
Density estimation deals with the problem of estimating probability density
functions based on some data sampled from the PDF. It may use assumed forms
of the distribution, parameterized in some way
Ph 129b
Probability and Statistics
OUTLINE
Frank Porter, 130103
1. Probability
(a) Denition
(b) Random Variables and Notation
(c) Basic Properties
(d) Statistical Independence
(e) Expectation Values
(f) Mean and Variance
(g) Some Important Probability Dis
Physics 129b
Winter 2013
Frank Porter
Revised 130103
Notes about course:
Physics 129b is devoted to probability and statistics.
I will provide course notes on the topics we will cover. These will be available on
the web page for the course, and are the
Physics 129a
Fall 2012
Course Notes
Revised 120902
Notes about course:
Physics 129a is devoted to what may loosely be called analysis.
Physics 129b is devoted to probability and statistics. Third quarter,
129c is devoted to group theory as used in physic
Physics 129a
Problem Set Number 10
Due Friday, December 14, 2012
Please turn in to Min-Feng Tus mail box on rst oor of Est Bridge. MinFeng will be grading this assignment.
42. The Helmholtz equation, part III: Exercise 11 in the Linear Dierential
Equation