python积分计算高等数学_Python符号计算：微积分

#coding:utf-8

'''

微积分

'''

import sympy

sympy.init_printing()

from sympy import I, pi, oo

import numpy as np

# 1、求函数的导数

x = sympy.Symbol('x')

y = sympy.Symbol('y')

z = sympy.Symbol('z')

f = sympy.Function('f')(x)

# 对函数f的变量x进行求导

print('diff x:',sympy.diff(f, x))

# 对函数f的变量x进行求解二阶导数和三阶导数

print('diff x:',sympy.diff(f, x, x))

print('diff x:',sympy.diff(f, x, 3))

# 对函数多个变量求不同阶次的导数

g = sympy.Function('g')(x, y)

result = g.diff(x, y)

result = g.diff(x,2,y,3)

# 具体函数求导实例

expr = x**4 + x**3 + x**2 + x + 1

# 求一阶导数

result = expr.diff(x)

# 求二阶导数

result = expr.diff(x, x)

expr = (x + 1)**3 * y ** 2 * (z - 1)

result = expr.diff(x, y, z)

# 三角函数求导

expr = sympy.sin(x * y) * sympy.cos(x / 2)

result = expr.diff(x)

# 特殊函数求导

expr = sympy.special.polynomials.hermite(x, 0)

result = expr.diff(x).doit()

d = sympy.Derivative(sympy.exp(sympy.cos(x)), x)

# 通过调用doit函数执行求导

result = d.doit()

# 2、积分

a, b, x, y = sympy.symbols("a, b, x, y")

f = sympy.Function("f")(x)

# 函数的积分

result = sympy.integrate(f)

# 函数在某个期间的积分

result = sympy.integrate(f, (x, a, b))

result = sympy.integrate(sympy.sin(x))

print('result = ',result)

print('result = ',sympy.integrate(sympy.sin(x), (x, a, b)))

result = sympy.integrate(sympy.exp(-x**2), (x, 0, oo))

print('result = ',result)

# 函数从某个值到无穷期间的积分

result = sympy.integrate(sympy.exp(-x**2), (x, 0, oo))

a, b, c = sympy.symbols("a, b, c", positive=True)

result = sympy.integrate(a * sympy.exp(-((x-b)/c)**2), (x, -oo, oo))