Creation a New Mathematics Relations Using Engineering Approaches

The mathematics laws, relations and functions are the guide for all the engineering designs and applications. This guide will simplified the work in the design phase but it capture the design in some times because the conditions of high accuracy in mathematics values. This accuracy not accepted any approximation in opposite side the values in the engineering fields that have small approximation in all times. This paper will propose a novel approach with its proves to replacement some complex functions with a more simplicity functions that have approximate general shape, then modified the alternative functions to approximate them values for all times, i.e. reduce the error (maximum and accumulated) between the original function and the alternative function. This paper discusses a new mathematics relation between some functions spatially the unintegralable functions such as arctan, arctanh, Gaussian and other functions. This relation will detect and prove using an engineering approach such as successive approximation in C++ programming also this paper will discuss the other derivatives for these relations if found. Finally it will give some important direct applications with some future expansions in this field.