(Casio Micropython/Numworks Python): Calculus
05-25-2020, 02:08 AM
Post: #1 Eddie W. Shore Senior Member Posts: 1,290 Joined: Dec 2013
(Casio Micropython/Numworks Python): Calculus
The following scripts creates the user functions for calculus:

f(x): define your function in terms of x here. This needs to be loaded into the script before running it. Each of the functions that follow will use f(x). You can call f(x) to evaluate the function at any value.

deriv(x): The approximate derivative at point x. The Five Stencil approximation is used.

sigma(a,b): Calculate the sum (Σ f(x)) from x = a to x = b.

integral(a,b,n): Calculates the definite integral ( ∫ f(x) dx) from x = a to x = b. The Simpson's rule is used with n divisions (n needs to be even)

solve(x0): Uses Newton's Rule to find roots for f(x).

Example

f(x) = -2x*^2 + 3x + 5
In Python: -2*x**2+3*x+5

f(0): 5
f(10): -165
f(-10): -225

deriv(10): -37.00004450971999

Σ f(x): x = 1 to 25: sigma(1,25): -8780

∫ f(x) dx: x = -3 to 1, n = 20: integral(-3,1,20): -10.666666666667

Solve f(x)=0, initial condition x0 = 2.5: solve(5): 2.5

Python Script: calculus.py

from math import *

Code:
# 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
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