Introduction to multivariable calculus

In Math 117 we were only taught functions of a single variable (eg: y = f(x)). In Math 119 we will be discussing functions of several variables

Introduction to f(x, y) §

Function of 2 variables f(x, y) maps a point $(x,y)\in {\mathbb{R}}^2$ to a point $f(x,y)\in \mathbb{R}$

The domain D(f) is a subset of ${\mathbb{R}}^2$ while the range R(f) is a subset of $\mathbb{R}$

The graph of a function $f:{\mathbb{R}}^2\to \mathbb{R}$ represents a surface in ${\mathbb{R}}^3$ defined by z = f(x, y)

Serge D’Alessio’s Math 119 Notes