## Overview

In an earlier lecture, we learned some foundations of object-oriented programming.

In an {doc}`earlier lecture <oop_intro>`, we learned some foundations of object-oriented programming.

The objectives of this lecture are

single: Object-Oriented Programming; Key Concepts

```

As discussed an earlier lecture, in the OOP paradigm, data and functions are **bundled together** into "objects".

As discussed an {doc}`earlier lecture <oop_intro>`, in the OOP paradigm, data and functions are **bundled together** into "objects".

An example is a Python list, which not only stores data but also knows how to sort itself, etc.

In this section, we look at some more formal details related to classes and `self`

* You might wish to skip to the next section the first time you read this lecture.

{doc}`the next section <oop_solow_growth>`* You might wish to skip to the first time you read this lecture.

* You can return to these details after you've familiarized yourself with more examples.

Methods actually live inside a class object formed when the interpreter reads

* $n$ is the population growth rate

* $\delta$ is the depreciation rate

A **steady state** of the model is a $k$ that solves `solow_lom` when $k_{t+1} = k_t = k$.

A **steady state** of the model is a $k$ that solves {doc}`solow_lom <solow_lom>` when $k_{t+1} = k_t = k$.

Here's a class that implements this model.

Some points of interest in the code are

* An instance maintains a record of its current capital stock in the variable `self.k`.

* The `h` method implements the right-hand side of `solow_lom`.

* The `update` method uses `h` to update capital as per `solow_lom`.

{doc}`solow_lom <solow_lom>`{doc}`solow_lom <solow_lom>`* An instance maintains a record of its current capital stock in the variable `self.k`.

* The `h` method implements the right-hand side of .

* The `update` method uses `h` to update capital as per .

* Notice how inside `update` the reference to the local method `h` is `self.h`.

The methods `steady_state` and `generate_sequence` are fairly self-explanatory

plt.show()

```

On the horizontal axis is the parameter $r$ in `quadmap2`.

On the horizontal axis is the parameter $r$ in {doc}`quadmap2 <quadmap2>`.

The vertical axis is the state space $[0, 1]$.

### Exercise 2

In an earlier exercise, you wrote a function for evaluating polynomials.

In an {doc}`earlier exercise <pyess_ex2>`, you wrote a function for evaluating polynomials.

This exercise is an extension, where the task is to build a simple class called `Polynomial` for representing and manipulating polynomial functions such as

\qquad (x \in \mathbb{R})

```

The instance data for the class `Polynomial` will be the coefficients (in the case of `polynom`, the numbers $a_0, \ldots, a_N$).

The instance data for the class `Polynomial` will be the coefficients (in the case of {doc}`polynom <polynom>`, the numbers $a_0, \ldots, a_N$).

Provide methods that

1. Evaluate the polynomial `polynom`, returning $p(x)$ for any $x$.

{doc}`polynom <polynom>`1. Evaluate the polynomial , returning $p(x)$ for any $x$.

1. Differentiate the polynomial, replacing the original coefficients with those of its derivative $p'$.

Avoid using any `import` statements.