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

pmb13005/roots_and_optimization

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