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Calculus: Concepts and Methods by Joan Davies, Ken Binmore

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Three

Functions of several variables

In this chapter we shall consider functions of two or more variables and extend the ideas developed for functions of one variable to such functions. We initially consider functions of two variables whose graphs can be visualised, before generalising to functions of more than two variables.

We define the concept of a partial derivative with respect to one of the variables and use it to find the equation of the tangent plane to a function at a point. The concept of the derivative of a function of several variables is then considered and a notation for the derivative introduced which accords with the rest of the ...

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