Welcome to Week 1! After an overview of the lecture, we will recall basic facts about polynomials and polynomial interpolation. Polynomials are an extremely useful class of function as they are simple to describe, and can approximate arbitrary continuous functions. We will then get to know a very useful class of polynomials, the Chebyshev polynomials. Some of their properties are illustrated with the MATLAB package Chebfun.

**Intended Learning Outcomes**

At the end of the week you should be able to:

- describe Horner’s method;
- describe the polynomial interpolation problem and it’s solution via Lagrange interpolation;
- know the statement of the Weierstrass interpolation problem and why it may not be useful in practice;
- derive important properties of Chebyshev polynomials.

**Tasks and Materials**

- Become familiar with a scientific computing system (MATLAB, Julia or Python), as described in the Computing section. If you are familiar with MATLAB,

then you might want to try out Chebfun.
- Have a look at the preliminaries document and the handouts for this week (in the Lectures section).
- The first problem sheet is available and will be discussed in Week 2.

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