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