calculus.py

Created by ews31415

Created on April 16, 2020

693 Bytes

Calculus, Derivative, Sum, Integral (Simpson’s Rule), Solve f(x) = 0 (Newton’s Method)


from math import *

# 2020-04-15 EWS

# define f(x) here
def f(x):
  return -2*x**2+3*x+5
  
# derivative
def deriv(x):
  # uses f(x), 5 stencil
  # h is tolerance
  h=1e-10
  d=(12*h)**-1*(f(x-2*h)-8*f(x-h)+8*f(x+h)-f(x+2*h))
  return d

# sum/sigma
def sigma(a,b):
  t=0
  n=b-a
  for i in range(n):
    t=t+f(i+1)
  return t

# integral by simpsons rule
def integral(a,b,n):
  t=f(a)+f(b)
  h=(b-a)/n
  for i in range(n-1):
    w=(i+1)/2
    if (w-int(w))==0:
      t=t+2*f(a+(i+1)*h)
    else:
      t=t+4*f(a+(i+1)*h)
  t=t*h/3
  return t

# solver
def solve(x0):
  tol=1e-14
  x1=x0-f(x0)/deriv(x0)
  while abs(x1-x0)>tol:
    x0=x1
    x1=x0-f(x0)/deriv(x0)
  return x1