### Introduction

Vector Calculus is the study of the various derivatives and integrals of a scalar or vector function of the variables defining position ( $x$ , $y$ , $z$ ) and possibly also time $\left(t\right)$ . This Section considers functions of several variables and introduces scalar and vector fields.

#### Prerequisites

- be familiar with the concept of a function of two variables
- be familiar with the concept of partial differentiation
- be familiar with the concept of vectors

#### Learning Outcomes

- state the properties of scalar and vector fields
- work with a vector function of a variable

#### Contents

1 Functions of several variables and partial derivatives2 Vector functions of a variable

3 Scalar fields

4 Vector fields