df['col2'] = df['col1'].map(lambda x: x**2)

define square(x): 
  return (x ** 2) 
 
df['col2'] = df['col1'].map(square) 

df['col3'] = df.apply(lambda x: x['col1'] + 2 * x['col2'], axis=1) 

In [44]: f = lambda x : x.max()-x.min()

In [45]: df.apply(f)
Out[45]:
data1  5.042275
data2  1.967290
dtype: float64

In [46]: df.apply(f,axis=1)
Out[46]:
0  2.810074
1  1.009774
2  0.537183
3  0.813714
4  1.750022
dtype: float64

In [47]: f = lambda x : x+1

In [48]: df.applymap(f)
Out[48]:
   data1   data2
0 -1.332263 1.477812
1 0.284755 1.294528
2 0.066644 0.603827
3 1.757402 2.571117
4 3.710012 1.959990

In [49]: df['data1']
Out[49]:
0  -2.332263
1  -0.715245
2  -0.933356
3  0.757402
4  2.710012
Name: data1, dtype: float64

In [50]: df['data1'].map(f)
Out[50]:
0  -1.332263
1  0.284755
2  0.066644
3  1.757402
4  3.710012
Name: data1, dtype: float64

df['col3'] = df.groupby('col1')['col2'].transform(lambda x: (x.sum() - x) / x.count()) 

sumcount = df.groupby('col1')['col2'].transform(lambda x: x.sum() + x.count()) 
df['col1'].map(sumcount) 

df['col2'] = df.groupby('col1').agg({'col1':{'col1_mean': mean, 'col1_sum‘': sum}, 'col2': {'col2_count': count}}) 

In [52]: df.agg(['mean','sum'])
Out[52]:
     data1   data2
mean -0.102690 0.581455
sum -0.513449 2.907274