Introduction to Computing Using Python

1. # Practice Problem 5.9
   
2. def add2D(t1, t2):
   
3.     '''t1 and t2 are 2D lists with the same number of rows and
   
4.        same number of equal sized columns
   
5. 
   
6.        add2D increments every item t1[i][j] by t2[i][j]'''
   
7.     nrows = len(t1)                # number of rows
   
8.     ncols = len(t1[0])             # number of columns
   
9.     for i in range(nrows):         # for every row index i
   
10.         for j in range(ncols):         # for every column index j
    
11.             t1[i][j] += t2[i][j]

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1. # Practice Problem 5.10
   
2. def interest(rate):
   
3.     '''returns the number of years for investment
   
4.       to double for the given rate'''
   
5.     amount = 100                 # initial account balance
   
6.     count = 0
   
7.     while amount < 200:
   
8.         # while investment not doubled in value
   
9.         count += 1               # add one more year
   
10.         amount += amount*rate    # add interest
    
11.     return count

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1. # Practice Problem 5.11
   
2. def approxE(error):
   
3.     'returns approximation of e within error'
   
4.     prev = 1                        # approximation 0
   
5.     current = 2                     # approximation 1
   
6.     i = 2                           # index of next approximation
   
7.     while current - prev > error:
   
8.         # while difference between current and previous
   
9.         # approximation is too large
   
10.                                     # current approximation
    
11.         prev = current              # becomes previous
    
12.                                     # compute new approximation
    
13.         current = prev + 1/factorial(i)  # based on index i
    
14.         i += 1                      # index of next approximation
    
15.   return current

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