## NEKG33 Mathematical methods for economists

## Chapter 25 : Day 25: Function of several variables.

### By Lund University

We have been working with functions of two variables a bit. But wait, there is more!

## Functions of several variables

We begin this section by looking at functions of two variables in more detail. The graph of a function of two variables will be a three dimensional figure. We extend this idea to functions with an arbitrary number of variables.

#### Functions of two variables

#### Graph of a function of two variables

#### Functions of several variables

## Functions of several variables: Problems

Exercises on functions of several variables

#### Problem: Find the natural domain of a function of two variables

#### Problem: Level curves

#### Problem: Intersection of level curves

## Partial derivatives

The first lecture is a review. We look at the formal definition of partial derivatives and how to collect second order partial derivatives into a Hessian. In the final lecture, we will look at the chain rule for functions of several variables.

#### Partial derivatives, rough introduction

#### Partial derivatives

#### Hessian

#### Chain rule for functions of two variables

## Partial derivatives: Problems

Exercises on partial derivatives and Hessian