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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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