16 Functions of More than One Variable – Partial Differentiation
This chapter deals with functions of more than one variable and the rates of change of
such functions as the different variables change. It involves some visualisation in three
dimensions, but on the other hand the manipulation and methods involved are usually
quite straightforward – essentially, there is little more to it than ordinary differentiation.
Prerequisites
It will be helpful if you know something about- function notation (90
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)- limits (412
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)- rules of differentiation (234
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)- three dimensional coordinates and graphs (323
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)- parametric differentiation (240
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)- implicit differentiation (238
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)Objectives
In this chapter you will find- functions of two variables
- definition of partial differentiation
- rules of partial differentiation
- higher order partial derivatives
- the total differential and total derivative
Motivation
You may need the material of this chapter for- thermodynamics
- partial differential equations
- vector calculus
- electromagnetic field theory
- fluid and solid mechanics
- least squares in statistics