Well Logging and Formation Evaluation
Covering all aspects of well logging and formation evaluation, this comprehensive guide offers practical techniques that will be valuable to petrophysicists and engineers in their day-to-day jobs.
TABLE OF CONTENTS Well Logging and Formation Evaluation
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:
This is the equation of a straight line having a gradient of a and intercept 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:
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:
| Function | dy/dx |
|---|---|
| y = x n + a ( n ? 0) | n* x n ? 1 |
| y = e x | e x |
| y = log( x) (log is natural logarithm base e) | 1/ x |
| y = sin( x) ( x must be in radians = deg* ?/180) | cos( x) |
| y = cos( x |
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