## 5

## Differential Calculus of Several Variables

##### 5.0 INTRODUCTION

There are many practical situations in which a quantity of interest depends on the values of two or more variables.

For example

- The volume of a circular cylinder is
*V* = *πr*^{2}*h*, where *r* is the radius of the base circle and *h* is the height of the cylinder. So, *V* is a function of two variables *r* and *h*.
- The volume of a rectangular parallelopiped is
*V* = *lbh*, where *l*, *b*, *h* are the length, breadth and height. Here *V* is a function of three variables *l*, *b*, *h*.

Similarly we can have functions of more than two or three variables. But, for simplicity, we shall deal with functions of two variables and the arguments and results can be extended to more than two variables.

##### 5.1 LIMIT AND CONTINUITY ...