Hello folks! In this tutorial, we are going to learn how we can plot mathematical functions using Python. So let’s get started.
Prerequisites
For plotting different mathematical functions using Python, we require the following two Python libraries:
1. NumPy
NumPy is a Python library that supports multi-dimensional arrays & matrices and offers a wide range of mathematical functions to operate on the NumPy arrays & matrices. It is one of the most fundamental libraries for scientific computation. We can install NumPy on our local computer using the following command.
> python -m pip install numpy
2. Matplotlib
Matplotlib is a Python library that is widely used for various types of plotting. Using Matplotlib, We can plot static and interactive visualizations very easily. We can install Matplotlib on our local computer using the following command.
> python -m pip install matplotlib
Steps to Plot Mathematical Functions
First import the numpy and matplotlib.pyplot module in the main Python program (.py) or Jupyter Notebook (.ipynb) using the following Python commands.
import numpy as np
import matplotlib.pyplot as plt
For all the plottings, we will follow almost the same steps apart from using the specific NumPy mathematical function in the respective plots.
1. Plot (y = x) Identity function
x = np.arange(0, 11, 1)
y = x
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Identity Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [ 0 1 2 3 4 5 6 7 8 9 10]
Values of y: [ 0 1 2 3 4 5 6 7 8 9 10]
2. Plot (y = a.x2 + b.x2 + c) Quadratic function
x = np.arange(-11, 11, 1)
a = 2
b = 9
c = 10
y = a*(x**2) + b*x + c
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Quadratic Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10]
Values of y: [153 120 91 66 45 28 15 6 1 0 3 10 21 36 55 78 105 136 171 210 253 300]
3. Plot (y = a.x3 + b.x2 + c.x + d) Cubic function
x = np.arange(-11, 11, 1)
a = 2
b = 3
c = 4
d = 9
y = a*(x**3) + b*(x**2) + c*x + d
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Cubic Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10]
Values of y: [-2334 -1731 -1242 -855 -558 -339 -186 -87 -30 -3 6 9 18 45 102 201 354 573 870 1257 1746 2349]
4. Plot (y = ln(x) or loge(x)) Natural logarithm function
x = np.arange(1, 11, 0.001)
y = np.log(x)
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Natural logarithm Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [ 1. 1.001 1.002 ... 10.997 10.998 10.999]
Values of y: [0.00000000e+00 9.99500333e-04 1.99800266e-03 ... 2.39762251e+00 2.39771344e+00 2.39780436e+00]
5. Plot (y = log10x) Common/Decimal logarithm function
x = np.arange(1, 11, 0.001)
y = np.log10(x)
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Common logarithm Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [ 1. 1.001 1.002 ... 10.997 10.998 10.999]
Values of y: [0.00000000e+00 4.34077479e-04 8.67721531e-04 ... 1.04127423e+00 1.04131372e+00 1.04135320e+00]
6. Plot (y = ex) Natural Exponential function
x = np.arange(-11, 11, 0.01)
y = np.exp(x)
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Natural exponential Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [-11. -10.99 -10.98 ... 10.97 10.98 10.99]
Values of y: [1.67017008e-05 1.68695557e-05 1.70390975e-05 ... 5.81045934e+04 5.86885543e+04 5.92783841e+04]
7. Plot (y = ax) General Exponential function
x = np.arange(-11, 11, 0.01)
a = 8
y = a**x
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("General exponential Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [-11. -10.99 -10.98 ... 10.97 10.98 10.99]
Values of y: [1.16415322e-10 1.18861455e-10 1.21358987e-10 ... 8.07043896e+09 8.24001604e+09 8.41315629e+09]
8. Plot (y = sign(x)) Signum function
x = np.arange(-11, 11, 0.001)
y = np.sign(x)
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Signum Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y)")
plt.show()
Output:
Values of x: [-11. -10.999 -10.998 ... 10.997 10.998 10.999]
Values of y: [-1. -1. -1. ... 1. 1. 1.]
9. Plot (y = a.sin(b.x + c)) Sinusoidal function in Python
x = np.arange(-11, 11, 0.001)
a = 5
b = 3
c = 2
y = a*np.sin(b*x + c)
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Sinusoidal Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [-11. -10.999 -10.998 ... 10.997 10.998 10.999]
Values of y: [ 2.02018823 2.03390025 2.04759397 ... -2.10016104 -2.11376421 -2.12734835]
10. Plot (y = sinc(x)) Sinc function
x = np.arange(-11, 11, 0.01)
y = np.sinc(x)
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Sinc function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [-11. -10.99 -10.98 ... 10.97 10.98 10.99]
Values of y: [1.41787526e-16 9.09768439e-04 1.82029537e-03 ... 2.73068428e-03
1.82029537e-03 9.09768439e-04]
11. Plot (y = cosh(x)) Hyperbolic function
x = np.arange(-11, 11, 0.001)
y = np.cosh(x)
print('Values of x: ', x)
print('Values of y: ', y)
plt.plot(x, y)
plt.title("Hyperbolic Function")
plt.xlabel("Values of x")
plt.ylabel("Values of y")
plt.show()
Output:
Values of x: [-11. -10.999 -10.998 ... 10.997 10.998 10.999]
Values of y: [29937.07086595 29907.14875865 29877.2565585 ... 29847.39423524 29877.25655813 29907.14875828]
Summing-up
In this tutorial, we have learned how to plot different types of mathematical functions using Numpy and Matplotlib libraries. Hope you have understood the plotting process of different mathematical functions and are ready to experiment on your own. Thanks for reading! Stay tuned with us for amazing learning resources on Python programming.