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