for u=<2,1,-3> and v=<1,0,2>,
a) find the angle between u and v
b) use the formula proj_a b=((a•b)/|b|^2)b to find vector
projection of v onto u
c) sketch vectors u, v, and the projection found with only using
arrows
d) find the area of the parallelogram determined by u and v
A) Describe an AR and an MA model. How are they related?
(15)
B) Explain the Hoderick-Prescot filter. (15)
C) Explain how you would identify an appropriate ARIMA structure
for a time series model. (20)
*Bragg Scattering
What is the Bragg Scattering angle (i.e. the angle, in degrees,
between the incoming incident beam and the reflected beam) for
electrons scattered from a nickel crystal if their energy is 63 eV?
The spacing between Ni Bragg planes is 0.215 nm. Give your result
to 3 significant figures.
Solve the linear system Az = b using the following methods:
I. The GE+PP algorithm for sparse (banded) linear systems, which
is the default algorithm used by Matlab’s “\” operator when the
matrix (call it Asparse) is of sparse type. You may find it easiest
to set up the matrix using the spdiags command.
(a) Solve the linear system Az = b using the following three
methods:
I. The GE+PP algorithm for sparse (banded) linear systems, which
is the default algorithm used by Matlab’s “\” operator when the
matrix (call it Asparse) is of sparse type. You may find it easiest
to set up the matrix using the spdiags command.
II. The GE+PP algorithm for dense linear systems, again using
“\”. Here, you need a dense version of A which you can obtain
either...