README.md

# Homework #3

| solver | initial guess(es) | ea | number of iterations|
| --- | --- | --- | --- |
|falsepos   |18.9189|    0.2152|   50.0000|
|incsearch  |17.9474|    0.0000|    9.0000|
|newtraph   |      0|         0|   49.0000|
|mod_secant |17.9474|    0.0000|    4.0000|

![Convergance plot for numerical solvers](convergance4functions.png)

## Description

#### func/hw3

Contains all functions used for Homework #3.

#### ME3255_HW3_roots.m

Finds the roots and compares the iterations required for each function.

#### ME3255_HW3_convergance.m

Creates the convergance plot be repeatedly calling to the various solvers.

#### convergance4functions.png

The plot ouput by ME3255_HW3_convergance.m

## Divergance

x_i = .2

|number of iterations| approximate error * 10e7| root |
| --- | --- | --- | --- |
|1|0.0000| -0.1116|
|2|0.0000| -0.0212|
|3|0.0002| -0.0009|
|4|0.0058| -0.0000|
|5|3.3152| -0.0000|

## Convergance

x_i = 2

|number of iterations| spproximate error| root |
| --- | --- | --- | --- |
|1|12.5000| 2.2857|
|2| 5.2205| 2.4116|
|3| 3.3683| 2.4957|
|4| 2.4708| 2.5589|
|5| 1.9397| 2.6095|

# Homework #4

## Description

#### func/hw4
Contains all functions used for Homework 4.
#### goldmin.m
The function described fully in lecture (taken from lecture 8 in ME3255S2017)
#### collar_potential_energy.m
The function created in part a. Calculates potential energy of the collar.
#### ME3255_HW4_mininumPE.m
The script used to run the goldmin function on collar_potential_energy.

![Steady-state position of collar on rod at angle theta](minPEplot.png)