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2016Summary.py

calcpage Jun 23rd, 2016 (edited) 940 Never
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1. #!/usr/bin/python
2. #MrG 2016.0624 Pythonic Calculus Executive Summary!
3. from math import sqrt,pi
4. from turtle import *
5.
6. #1) define a function, ie f(x)=x**2-2
7. def f(x):
8.     return x**2-2
9. print "f(sqrt(2)) = ", f(sqrt(2))
10.
11. #2) find the numerical derivative as a limit
12. def diff(x,h):
13.     return (f(x+h)-f(x))/h
14.
15. print
16. print "f'(2) = "
17. for x in range(5):
18.     print diff(2,10**-x)
19.
20. #3) find roots using newton's method as a limit
21. def root(g):
22.     return g-f(g)/diff(g,10**-6)
23.
24. print
25. print "the closest root of f(x)==0 near x=1 is:"
26. g=1
27. for x in range(5):
28.     print g
29.     g=root(g)
30.
31. #4) find the definite integral as a limit
32. print
33. print "the definite integral of f(x) from 0 to pi ="
34. a=float(0)
35. b=pi
36. for x in range(5):
37.     n=10**x
38.     h=(b-a)/n
39.     l=sum([f(a+i*h)*h for i in range(n)])
40.     r=l-f(a)*h+f(b)*h
41.     print (l+r)/2
42.
43. #5) plots using turtle.py package from idle
44. #5) f(x)=x**2-2 ==> f(1)==-1
45. #5) f'(x)=2*x ==> f'(1)==2
46. #5) tangent line to f(x) at x=1 is:
47. #5) y-y1==m*(x-x1) ==> y-f(x1)==f'(x1)*(x-x1)
48. #5) y+1==2*(x-1) ==> y+1==2*x-2 ==> y=2*x-3
49. def g(x):
50.     return 2*x-3
51.
52. def plot(size):
53.     #canvas
54.     setworldcoordinates(-size,-size,size,size)
55.     #hide turtle
56.     ht()
57.     # x-axis
58.     pu()
59.     color("green")
60.     setpos(-size,0)
61.     pd()
62.     fd(2*size)
63.     # y-axis
64.     pu()
65.     color("green")
66.     setpos(0,-size)
67.     rt(270)
68.     pd()
69.     fd(2*size)
70.     # plot f(x)
71.     pu()
72.     color("red")
73.     setpos(-size,f(-size))
74.     pd()
75.     x=-size
76.     while x <= size:
77.         x+=0.1
78.         goto(x,f(x))
79.     # plot g(x)
80.     pu()
81.     color("blue")
82.     setpos(-size,g(-size))
83.     pd()
84.     x=-size
85.     while x <= size:
86.         x+=0.1
87.         goto(x,g(x))
88.     #delay
89.     mainloop()
90.
91. plot(3)
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