2.4. Functions#

Functions are pieces of code that we will want to use numerous times. This could be as simple as \(f(x) = sin(x)\), or something much more complicated.

2.4.1. Learning goals#

After this notebook, you should be able to

  1. Define a python function

  2. Use a python function

2.4.2. Syntax#

If we want to compute \(f(x) = sin(x)\) numerous times throughout our code or our notebook, it can be useful to define a function that performs this manipulation and returns the result. The syntax for this is

def function_name(arguments):

Tabbed in below the definition, you write the lines of code that you want to perform. Importantly, the last line should read

return some_value

where your code needs to have defined variable some_value prior to the return line. This line returns this value just like \(f(x)\) returns the value of \(f\) at position \(x\).

I will define a couple of example functions below

import numpy as np
def function_sin(x):
    return np.sin(x)

x = np.pi/4
print("sin(pi/4) = ", function_sin(x))

sin(pi/4) =  0.7071067811865475

Now this function is a bit silly for two reasons. First is that the function is pretty simple so it is not really necessary to define a function to do this manipulation. Second, our function actually just calls a numpy function for sin. We didn’t really write our own. But that is ok for now.

def polynomial_function(x):
    return x**5 + 4*x**2 - 2*x + 6

x = 3
print("3^5 + 4*3^2 - 2*3 +6 = ", polynomial_function(x))

3^5 + 4*3^2 - 2*3 +6 =  279

2.4.3. Functions with more than one argument#

You can feed multiple arguments to fuction. This could be because your function has more than one variable, e.g. \(f(x,y)\), or because there are parameters/constants that need to be fed to the function at different times.

We will use the ideal gas law as an example: \(PV = nRT\). This can be written as \(P\) as a function of \(n, V, T\)

(2.1)#\[\begin{equation} P(n,V,T) = \frac{nRT}{V} \end{equation}\]

but we see that we also have \(R\), the universal gas constant to deal with. The value of this constant will depend on the units that you are using for volume and the desired units of pressure.

def p_ideal(n, V, T, R):
    return n*R*T/V

R = 0.08206 # units of L atm mol^{-1} K^{-1}
n = 1       # units of mol
T = 300     # K
V = 22.4    # L
print("P(1mol, 22.4 L, 300K) = ", p_ideal(n,V,T,R), "atm")

P(1mol, 22.4 L, 300K) =  1.099017857142857 atm