June 2003
Intermediate to advanced
576 pages
18h 29m
English
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17
Functions of more than one variable
17.1 Introduction
We concentrated so far in this book on functions of time. In Chapter 5 we looked at waves that were functions of distance, x, and time, t. For many applications, we need to analyse functions of the three possible spatial coordinates, x, y, and z and also of time, t. For instance, consider making a mug of tea using a tea bag. When first brewed, the temperature will be nearly at boiling point 100°C. The temperature of the water will start off being much the same everywhere but it will be cooler near the tea bag and at the sides of the mug. As time progresses the surface of the tea and those parts in touch with the mug, will cool quicker than the centre of the tea. We can see that the temperature ...
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