### Introduction

Polynomials are functions with useful properties. Their relatively simple form makes them an ideal candidate to use as approximations for more complex functions. In this second Workbook on Numerical Methods, we begin by showing some ways in which certain functions of interest may be approximated by polynomials.

#### Prerequisites

- revise material on maxima and minima of functions of two variables
- be familiar with polynomials and Taylor series

#### Learning Outcomes

- interpolate data with polynomials
- find the least squares best fit straight line to experimental data

#### Contents

1 Polynomials2 Taylor series

3 Polynomial approximations - exact data

3.1 Lagrange interpolation

3.2 Error in Lagrange interpolation

4 Polynomial approximations - experimental data

5 Polynomial approximations - splines