Homework 1
1) Create your own homepage. It should be well-structured and include at least
one picture and one link to another website or subdirectory. Include something
special that will make your webpage stand out. (25 points)
2)Data Fitting:
Use Xmgrace to solve this problem. Consider the 5 sets of measurements in the
table below. What are the functional forms for f(x), g(x), h(x), i(x) and j(x)
that best fit each set? Make a plot of the data along with the fits, i.e. the
data given in the table below should be shown as symbols, and the fits as solid
lines. Put labels on the x- and y-axes. (25 points)
|
x |
f(x) |
g(x) |
h(x) |
i(x) |
j(x) |
|
0.0 |
0.00 |
0.00 |
3.00 |
0.00 |
0.00 |
|
0.5 |
0.63 |
1.59 |
8.15 |
1.68 |
1.00 |
|
1.0 |
5.00 |
2.00 |
22.17 |
1.82 |
1.50 |
|
1.5 |
16.88 |
2.29 |
60.26 |
0.28 |
1.50 |
|
2.0 |
40.00 |
2.52 |
163.79 |
-1.51 |
1.00 |
|
2.5 |
78.13 |
2.71 |
445.24 |
-1.92 |
0.00 |
3) Mathematica Problem:
(i) use Mathematica to numerically solve the transcendental equation for the
magnetization m as a function of the reduced temperature t
in an Ising ferromagnet: m=tanh(m/t) .Print out a
copy of your Mathematica protocol and attach it to your homework.
(ii) Expand the above equation around t=0 and around m=0,
i.e. for small temperatures and for small magnetizations.
(iii) Plot these approximations along with the full solution obtained in (i),
using a graphics program of your choice, i.e. Xmgrace or Mathematica.
(50 points)