5 Python Modules for Scientific Computing

Let’s take a look at the capabilities and features of the module concept in Python; we’ll describe five scientific computing modules in a keyword-like manner.


Instead of module, the terms library or software library are also commonly used. The capabilities of Python are best illustrated by using short sample programs. Of course, you don’t need understand the source code shown in this blog post. This is just to introduce you to the different modules.



The NumPy module (numerical Python) enables you to perform extensive numerical calculations. For example, you can solve linear systems of equations, even with complex numbers. Below shows a simple vector calculus program.


01 import numpy as np

02 A=np.array([1, 2, 3])

03 B=np.array([4, 5, 6])

04 print("Vector       A:",A)

05 print("Vector       B:",B)

06 print("Total        A+B:",A+B)

07 print("Product      A*B:",A*B)

08 print("Cross product :",np.cross(A,B))

09 print("Scalar product:",,B))



Vector A: [1 2 3]

Vector B: [4 5 6]

Total    A+B: [5 7 9]

Product              A*B: [ 4 10 18]

Cross product : [-3 6 -3]

Scalar product: 32



The Matplotlib module allows you to display mathematical functions, histograms, and many other diagram types as well as to simulate and animate physical processes. The graphical design options are remarkably diverse and rich in detail. Below shows a simple example of the function plot of a polynomial.


01 import numpy as np

02 import matplotlib.pyplot as plt

03 x=np.arange(-2,6,0.01)

04 y=x**3-7*x**2+7*x+15

05 plt.plot(x,y)




This figure shows the output of the function plot.


A Function Plot Created Using Matplotlib



Using SymPy (symbolic Python), you can calculate integrals or derivatives symbolically or solve differential equations symbolically. A simplification of mathematical terms is also possible (and much more). The code below shows a simple example of symbolic differentiation and integration.


01 from sympy import *

02 x=symbols("x")

03 y=x**3-7*x**2+7*x+15

04 y_1=diff(y,x,1)

05 y_2=diff(y,x,2)

06 y_3=diff(y,x,3)

07 Y=integrate(y,x)

08 print("1. Derivative:",y_1)

09 print("2. Derivative:",y_2)

10 print("3. Derivative:",y_3)

11 print("   Integral :",Y)



  1. Derivative: 3*x**2 - 14*x + 7
  2. Derivative: 2*(3*x - 7)
  3. Derivative: 6

Integral : x**4/4 - 7*x**3/3 + 7*x**2/2 + 15*x



SciPy (scientific Python) allows you to numerically differentiate, integrate, and numerically solve systems of differential equations. SciPy is as comprehensive as it is versatile. The capabilities of SciPy can only be partially described in this book. Below is a simple example of a numerical integration program.


01 import scipy.integrate as integral

02 def f(x):

03          return x**2

04 A=integral.quad(f,0,5)

05 print("Area A=",A[0])



Area A= 41.66666666666666



Using VPython, you can display fields in a 3D view or even animate their movements in 3D space. As of version 7, the animations are displayed in the standard browser after the program starts. The final listing shows an example of how you can program the animation of a bouncing ball.


01 from vpython import *

02 r=1. #radius

03 h=5. #height

04 scene.background=color.white


06 box(pos=vector(0,0,0),size=vector(2*h,r/2,h),

07 ball = sphere(radius=r, color=color.yellow)

08 ball.pos=vector(0,2*h,0) #drop height

09 ball.v = vector(0,0,0) #initial velocity

10 g=9.81

11 dt = 0.01

12 while True:

13          rate(100)

14          ball.pos = ball.pos + ball.v*dt

15          if ball.pos.y < r:

16                    ball.v.y = -ball.v.y

17          else:

18                    ball.v.y = ball.v.y - g*dt



The figure below shows a snapshot of the animation.


A Bouncing Ball Animation Created Using VPython


Editor’s note: This post has been adapted from a section of the book Python for Engineering and Scientific Computing by Veit Steinkamp.


Python for Engineering and Scientific Computing
Python for Engineering and Scientific Computing

It’s finally here—your guide to Python for engineers and scientists, by an engineer and scientist! Get to know your development environments and the key Python modules you’ll need: NumPy, SymPy, SciPy, Matplotlib, and VPython. Understand basic Python program structures and walk through practical exercises that start simple and increase in complexity as you work your way through the book. With information on statistical calculations, Boolean algebra, and interactive programming with Tkinter, this Python guide belongs on every scientist’s shelf!

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Rheinwerk Computing
by Rheinwerk Computing

Rheinwerk Computing is an imprint of Rheinwerk Publishing and publishes books by leading experts in the fields of programming, administration, security, analytics, and more.