old_contents: '''
  Kaya Baber
  Physics 440 - Computational Physics
  Assignment 5 - PDEs
  Exploration 1 - Parabolic PDEs: Thermal Diffusion
  '''
  
  import numpy as np
  from numpy import linalg as LA
  import matplotlib.pyplot as plt
  import math
  
new_contents: '''
  Kaya Baber
  Physics 440 - Computational Physics
  Assignment 5 - PDEs
  Exploration 1 - Parabolic PDEs: Thermal Diffusion
  '''
  
  import numpy as np
  from numpy import linalg as LA
  import matplotlib.pyplot as plt
  import math
  
  
  
  
  #make banded matrix 
  #initialize column vector 
  #matrix multiply
  #modifiy boundaries
  #repeat
  
  
  
  def make_banded(N,M):
      bandTopBot = [2 + (4*M)/(N**2) ]*(N-1)
      bandMid = [-2.0/ (stepSize**2)]*N
      
      banded = np.diag(bandMid)
      banded = np.add(banded,np.diag(bandTopBot,1))
      banded = np.add(banded,np.diag(bandTopBot,-1))
      return banded
      
      
  #banded.dot(thermalArray)
  
subject: Set up the procedure to code out