# Project 5 for the University of Tulsa's CS-7863 Sci-Stat Course
# Systems of Equations and Finite Difference Methods
# Professor: Dr. McKinney, Spring 2023
# Noah L. Schrick - 1492657

## 1. Systems of Equations in Matrix Form
# a. Use built-in R solve

# b. Verify with matrix mult

## 2. Matrix from polynomial
# a. Create vector  for x and y

# b. Create coefficient matrix

# c. Solve 

# d. Plot

## 3. Kirchoff
# a. Create vectors
# Resistance vec
# Voltage vec
# Matrix A and vector b
# Solve
# Show currents

# b. Repeat a. Use V=200, and R=(5,10,5,15,0,20)

## 4. Schrodinger eq
#a. Solve and plot the 1d quantum harmonic oscillator wave function

# b. Solve with Shooting Method

## 5. Solve harmonic oscillator Schrodinger with finite difference
# a. Solve with R and Julia

# b. Solve damped oscillator with perturbation param
# Plot

## 6. Solve heat diffusion equation

# EC. Solve the square plate problem