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APPENDIX 4
ADDITIONAL
MATHEMATICS THEORY
For readers who do not have a mathematics, engineering, or physics
degree, some of the basic mathematical principles assumed in this book
may be problematic. Therefore, this Appendix is designed to provide a
fuller explanation of some of the theoretical derivations used in the
chapters.
A4.1 CALCULUS
Differentiation is the taking of the gradient of a function with respect
to one of the input variables. Start by considering the function:
+
y = a x b.
*
This is the equation of a straight line having a gradient of a and inter-
cept on the y axis at b.
The differential of y with respect to x is a function that describes the
rate of change of y with x. It is denoted by dy/dx, where d represents the
infinitesimally small increments of y and x. For the function given:
dy dx = a.
For most functions that engineers encounter, the differentials are simply
known by heart, or can be looked up in mathematical handbooks. Table
A4.1 gives most of the functions one is likely to come across:
It is also possible to take the differential of dy/dx, in which case the
2
2
result is referred to as d y/dx or d/dx(dy/dx). Where a function depends
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