README.md

# Homework #4

a. File collar_potential_energy.m solves for the total potential energy of the collar on the rod given a position and angle.

b. Solved using HW4_part_b_script.m

c. Solved using HW4_part_c_script.m - image sent via email

# Homework #3
i. Compare the number of iterations that each function needed to reach an
accuracy of 0.00001%. Include a table in your README.md with:

```
| solver | initial guess(es) | ea | number of iterations|
| --- | --- | --- | --- |
|falsepos   |  |  |  |
|bisect     |  |  |  |
|newtraph   |  |  |  |
|mod_secant |  |  |  |
```

ii. Compare the convergence of the 4 methods. Plot the approximate error vs the
number of iterations that the solver has calculated. Save the plot as
`convergence.png` and display the plot in your `README.md` with:

`![Plot of convergence for four numerical solvers.](convergence.png)`

iii. In the `README.md` provide a description of the files used to create the
table and the convergence plot. 

### divergence of Newton-Raphson method

| iteration | x_i | approx error |
| --- | --- | --- |
| 0 | 2 | n/a |
| 1 | 2.1429  |   .0667  |
| 2 | 2.2651  | .0539    |
| 3 |  2.3730 |  .0455   |
| 4 | 2.4705  |   .0395  |
| 5 |  2.5597 |   .0349  |

### convergence of Newton-Raphson method

| iteration | x_i | approx error |
| --- | --- | --- |
| 0 | .2 | n/a |
| 1 | -0.8870  |   1.2255  |
| 2 | .8671  |  2.0349   |
| 3 | 2.9885  |  0.7132   |
| 4 |  3.0479 |  0.0195   |
| 5 | 3.1047  |  0.0183   |