C. Maclaurin. A Scottish mathematician gained his master degree at age 17, and his major mathematics' work arise from his special knowledge in Newton's ideas and the formulation of Newton's methods.
However, C. Maclaurin also contributed to the astronomy science and helped to improve maps and invented some mechanical devices.
My mathematics python's programs is a set of Maclaurin's series to compute some of the most important functions in calculus.
Though, the computation of an infinite sum which give the value of a function in terms of the derivatives evaluated at a special case where x0 = 0,in contrast with Taylor series.
It is assumed that the angle is expressed in radian while using the Maclaurin's series to approximate the trigonometric functions sine and cosine, thus, converting the angle into degrees in my program could be useful for students who prefer using degrees.
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | #On the name of ALLAH and may the blessing and peace of Allah
#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Author : Fouad Teniou
#Date : 06/07/10
#version :2.6
"""
maclaurin_sin is a function to compute sin(x) using maclaurin series
and the interval of convergence is -inf < x < +inf
sin(x) = x - x^3/3! + x^5/5! - x^7/7! ...........
"""
from math import *
def maclaurin_sin(value,k):
"""
Compute maclaurin's series approximation for sin(x)
"""
global first_value
first_value = 0.0
#attempt to Approximate sin(x) for a given value
try:
for item in xrange(1,k,4):
next_value = (value*pi/180)**item/factorial(item)
first_value += next_value
for item in xrange(3,k,4):
next_value = -1*(value*pi/180)**item/factorial(item)
first_value += next_value
return first_value
#Raise TypeError if input is not a number
except TypeError:
print 'Please enter an integer or a float value'
if __name__ == "__main__":
maclaurin_sin1 = maclaurin_sin(70,100)
print maclaurin_sin1
maclaurin_sin2 = maclaurin_sin(45,100)
print maclaurin_sin2
maclaurin_sin3 = maclaurin_sin(30,100)
print maclaurin_sin3
#####################################################################
#"C:\python
#0.939692620786
#0.707106781187
#0.5
#####################################################################
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