Short Lesson: Math Operations

2. Short Lesson: Math Operations#

This notebook just highlights a couple of useful constants and functions we will use all the time. It assumes you know how to perform simiple math operations at this point.

Reminder \(\text{**}\) means power not “^”.

5**2

5^2  #this does not mean power as you can see from output

First thing we do is import the numpy extension and the scipy.constants extension which has a lot of useful mathematical functions. A link to the numpy documentation can be found under the jupyter Help menu.

import numpy as np 
from scipy import constants

Some available constants:

np.e  
np.pi
constants.e  
constants.pi
constants.R
constants.N_A
constants.k

np.e # this "e" is the base of the natural logarithm

2.718281828459045

constants.e # notice that this "e" is the charge on an electron

1.6021766208e-19

Some available functions:

np.cos(), np.sin(), np.arcsin(),  etc.
np.log(), np.log10(), np.sqrt(), etc.
np.mean(), np.sum(), np.median(), etc

General Math: https://numpy.org/devdocs/reference/routines.math.html

Statistics: https://numpy.org/devdocs/reference/routines.statistics.html

np.cos(np.pi)

-1.0

np.log10(100)

2.0

We can use sympy if we want to perform symbolic manipulation such as derivatives, integration, solving equations, etc. We will look at that later in the course.

np.sqrt(9)

3.0

np.random.randn(3)

array([-1.27598594, -0.9301613 ,  0.39859151])

np.random.random((3))

array([0.94765948, 0.27808895, 0.89048267])

np.random.randint(3,10, size=100) #notice that 3,10 gives numbers from 3,9

array([9, 5, 9, 8, 6, 6, 9, 7, 6, 9, 3, 9, 6, 8, 4, 3, 3, 6, 4, 9, 3, 5,
       6, 8, 7, 3, 6, 8, 3, 5, 5, 3, 7, 5, 8, 7, 4, 4, 4, 3, 6, 6, 7, 6,
       4, 5, 5, 5, 4, 9, 6, 8, 5, 6, 3, 5, 9, 7, 3, 6, 7, 3, 4, 8, 8, 5,
       8, 3, 5, 6, 4, 7, 6, 3, 5, 6, 9, 3, 6, 7, 3, 4, 5, 3, 3, 9, 6, 4,
       4, 7, 9, 8, 9, 3, 3, 4, 8, 9, 3, 6])