Advanced Mathematics and Python implementation

One: Chapter One:

Basic elementary functions:

. 1  Import numpy AS NP
 2  Import PANDAS AS PD
 . 3  Import matplotlib.pyplot AS PLT
 . 4  
. 5  Import Represents warnings
 . 6 warnings.filterwarnings ( ' the ignore ' )   # no warning 
. 7  
. 8  # mapping function 
9  # power function 
10  IF 0:
 . 11      X np.linspace = (-np.pi, 2 * np.pi, NUM = 50 )
 12 is      Y = X ** 2
 13 is  
14      plt.scatter (X, Y, marker = ' . ' )
 15     plt.plot (X, Y)
 16  
. 17      # auxiliary line 
18 is      plt.axvline (0, Color = ' Cyan ' , lineStyle = ' - ' , Alpha = 0.8 )
 . 19      plt.axhline (0, Color = ' Cyan ' , = lineStyle ' - ' , Alpha = 0.8 )
 20 is  
21 is  
22 is      plt.show ()
 23 is      Pass 
24  # exponential function 
25  IF 0:
 26 is      X = np.linspace (-np.pi, 2 * np.pi, NUM = 50 )
 27      Y = X 2 **   #Exponential function 
28  
29      plt.scatter (X, Y, marker = ' . ' )
 30      plt.plot (X, Y)
 31 is  
32      plt.axhline (0, Color = ' Cyan ' , lineStyle = ' - ' , Alpha = 0.8 )
 33 is      plt.axvline (0, Color = ' Cyan ' , lineStyle = ' - ' , Alpha = 0.8 )
 34 is  
35      plt.show ()
 36      Pass 
37 [  
38 is  # logarithmic function 
39  IF 0:
 40     x = np.linspace(-np.pi,2*np.pi,num= 50)
41     y = np.log2(x)
42 
43     plt.scatter(x,y,marker = '.')
44     plt.plot(x,y)
45 
46     plt.axhline(0,color='cyan',linestyle = '--',alpha = 0.8)
47     plt.axvline(0,color='cyan',linestyle = '--',alpha = 0.8)
48 
49     plt.show()
50 
51 
52 
53     pass
54 
55 #三角函数
56 if 0:
57     x = np.linspace(-np.pi,2*np.pi,num=50)
58     y = np.sin(x)
59 
60     plt.scatter(x,y,marker ='.')
61     plt.plot(x,y)
62 
63     plt.axhline(0,color = 'cyan',linestyle ='--',alpha = 0.8)
64     plt.axvline(0,color='cyan',linestyle = '--',alpha = 0.8)
65 
66     plt.show()
67 
68     pass
69 
70 #反三角函数
71 if 0:
72     #f = arcsin(x)
73     x = np.linspace(-np.pi,2*np.pi,num = 100)
74     y = np.arccos(x)
75 
76     plt.scatter(x,y,marker = '.')
77     plt.plot(x,y)
78 
79     plt.axhline(0,color='cyan',linestyle='--',alpha = 0.8)
80     plt.axvline(0,color='cyan',linestyle='--',alpha = 0.8)
81 
82     plt.show()
83     pass

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Limit the number of columns and functions:

. 1  Import numpy AS NP
 2  Import PANDAS AS PD
 . 3  Import matplotlib.pyplot AS PLT
 . 4  
. 5  # Import Represents warnings 
. 6  # warnings.filterwarnings ( 'the ignore') # no warning 
. 7  
. 8  # columns x / (x + 1) limit 
9  IF 0:
 10      X = np.arange (50 )
 . 11      Y = X / (X +. 1 )
 12 is  
13 is      plt.scatter (X, Y, marker = ' . ' )
 14      plt.plot (X, Y)
 15  
16      PLT .axvline (0, Color = 'Cyan ' , lineStyle = ' - ' , Alpha = 0.8 )
 . 17      plt.axhline (0, Color = ' Cyan ' , lineStyle = ' - ' , Alpha = 0.8 )
 18 is  
. 19      plt.show ()
 20 is  
21 is      Pass 
22 is  
23 is  # limit function 
24  IF 0:
 25      X = np.linspace (-2,2, NUM = 100 )
 26 is      Y = X -1 2 **
 27  
28      plt.scatter (X, Y, marker = ' . ' )
 29      plt.plot (x, y)
30  
31 is      plt.axvline (0, Color = ' Cyan ' , lineStyle = ' - ' )
 32      plt.axhline (0, Color = ' Cyan ' , lineStyle = ' - ' )
 33 is  
34 is      # limit 
35      plt.axhline (-1, Color = ' Red ' , lineStyle = ' - ' )
 36      plt.show ()
 37 [      Pass 
38 is  
39  
40  # exercise: limit 
41  # limit function 
42 is  IF. 1 :
 43 is      X = np.arange (1,50 )
 44 is      Y = (. 1 + 2 * X) / X
 45  
46 is      plt.scatter (X, Y, marker = ' . ' )
 47      plt.plot (X, Y)
 48  
49      # plt.axhline (2) # default color is similar to Cyan 
50      plt.axhline (2, color = ' Red ' ) # default straight line 
51 is  
52 is  
53 is      plt.show ()
 54 is      Pass

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