Download Course Wrapup Physics 3730/6720 Spring Semester 2016

Course Wrapup
Physics 3730/6720
Spring Semester 2016
Final Project Comments
Critical Frequency
Critical sampling
(Nyquist) of sine
wave is two per
cycle.
fc =1/(2t)
Frequencies
above this are
undersampled;
discrete FT is in
trouble!
Figures from Stephen Smith, Digital Signal Processing
Discrete Fourier Transforms
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Suppose that we have N sampled values
(further, suppose N is even)...
Now note that with N numbers input, we can
produce at most N numbers output. (Why?) The
most interesting range is -fc→ fc, so we'll want to
estimate frequency components at the discrete
values:
Intensity
#bins = #bins in time domain
-0.00833
0.0
f(Hz)
+0.00833
Announcements
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Due to 3740 final, Final Project due date is
pushed back to Sunday May 1st Midnight
th
I will be in SP 205 at 9:00 AM April 28 for
consultation about project, final exam, etc.
Final Exam
Wednesday May 4 , 8:00-10:00 AM
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Similar format to midterm:
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th
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Open book, notes, internet
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Consult only with instructor
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Online submission a la assignments.
nd
Focus on 2 half of semester, but
“comprehensive” as needs be.
Midterm Topics
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(Basic Unix and Emacs)
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sort, awk, sed
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Plotting with gnuplot
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Basic shell scripts
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Basic html
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C++
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math operations
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input/output
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conditionals, loops
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pointers, references
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random number generators
Program and plot with Python
Potential (Major) Final Exam Topics
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Statistics; Binomial, Poisson, Gaussian
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Numerical integration; trapezoid, Monte Carlo...
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Least-squares fitting
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Likelihood fitting
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ODEs (Euler, Runge-Kutta...)
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Discrete Fourier Transforms
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Maple (plotting, Matrix algebra)
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LaTex
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Python
Binomial Distribution
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The probability PB of observing  successes in N
trials, where the probability of success per trial
is p, is given by:
The average number of successes:
The standard deviation of the number of
successes  is given by:
Midpoint Rule
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Divide x-axis into
intervals of width h.
Use midpoint of
each interval to
compute area.
Error
The “Monte Carlo” Technique
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Employ's random
numbers to
determine
integrals.
e.g. what is the
area of a circle?
What is ?
 = 4x(709/900)
= 3.151 ± 0.055
Evaluating Fits: 
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2
Definition of 2
Absolute magnitude of 2 only has meaning
relative to the number of degrees of freedom
#DOF = (# of data points) (# parameters determined from the data)
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#DOF = (# of data points) - (# constraints)
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2 /#DOF ~ 1 for good fit
LaTex Math
I can put mathematical characters in a sentence by putting a dollar
sign before and after the characters. The area $A$ of a circle is
given by $A = \pi r^2$. I can also set equations apart from the
text as in the following example:
\begin{equation}
A = \pi r^2
\end{equation}
Note that latex will keep track of equation numbers for me.
Integrate ODEs:
Graphical Explanation
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A is initial point.
Euler uses derivative at
A to find approximation
to y(t+h) at B
Modified Euler uses
average of derivatives
at A and B to find
better approximation C