The Calculus for Engineers And Physicists : Integration And Differentiation, With Applications to Technical Problems And Classified Reference Tables of Integrals And Methods of Integration

Cover The Calculus for Engineers And Physicists : Integration And Differentiation, With Applications to Technical Problems And Classified Reference Tables of Integrals And Methods of Integration
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Geometrical Illustration of Two Independent Variables.
— Hitherto there have been considered combinations of such functions alone as are mutually dependent on each other. The functions x, X, M, etc., have been such that no one of them can change in size without the others concurrently, changing size.
In fig. 1, § 11, we have a vertical plane section of the surface of a piece of undulating land. Suppose it to be a meridional or north and south section. On it each distance measured northwards fro
...m a given starting-point corresponds to a definite elevation of the ground. If we take other meridional sections of the same piece of country, this same northward co-ordinate will correspond with other heights in these other sections. Thus, if h be used as a general symbol to mean the height of the surface at any and every point of it, then h depends not only on the northward co-ordinate INDEPENDENT VAEIABLES. 93 or latitude, but also upon the westward co-ordinate or longitude.
If there be freedom to move anywhere over the surface, the two co-ordinates of latitude and longitude may be varied independently of each other, that is, a change in one does not necessitate any change in the other.


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