While polynomials are a useful class of functions, they do have their limitations, and therefore we will start looking at rational approximations. One useful method of approximation using rational functions (ratios of polynomials) is Padé approximation. We will introduce this concept, show how one can compute and evaluate such an approximation, and discuss an example.

**Intended Learning Outcomes**

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

- describe the rational approximation problem and the concept of Padé approximation.
- compute and evaluate Padé approximants efficiently.

**Tasks and Materials**

- The third problem sheet is available and will be discussed this week, please have a look at it before class! Solutions to the previous problem sheet have been provided.

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