python 수학

 

pip install setuptools

 

 

함수 그래프

y = 2x + 3  (* x의 범위는 -5 ~ 5)

 

from sympy import *

from sympy.plotting import plot

x = symbols('x')

f = 2 * x + 3

plot(f, (x, -5, 5))

 

 

f = x² + 1

 

x = symbols('x')

f = x ** 2 + 1

plot(y, (f, -5, 5))

 

 

f = e^x

 

x = symbols('x')

f = exp(x)

plot(f, (x, -5, 5))

 

f = 2x + 3y

 

from sympy import *

from sympy.plotting import plot3d

x = symbols('x')

y = symbols('y')

f = 2 * x + 3 * y

plot3d(f)

 

 

 

미분

y = x² + 1

 

x = symbols('x')

y = x**2 + 1

dy_dx = diff(y)

 

print(dy_dx)

>> 2**x

 

 

체인룰

z에 대해 x를 미분은 아래와 같이 표현된다.

 

from sympy import *

from sympy.plotting import plot3d

x = symbols('x')

y = symbols('y')

# dy/dx

_y = x**2 + 1

dy_dx = diff(_y)

# dz/dy

z = y**3 - 2

dz_dy = diff(z)

# dz/dx -> dy_dx * dz_dy 결과에서 y 를 _y 로 치환

dz_dx_chain = (dy_dx * dz_dy).subs(y, _y)

print(dz_dx_chain)

>> 6*x*(x**2 + 1)**2

 

 

적분

 

f = x**2 + 1

plot(f, xlim=(-2,2), ylim=(0,2))

area = integrate(f, (x, 0, 1))

 

print(area)

>> 4/3