In this document we examine theories for the mechanics of helical springs, stress in structures and methods for calculating Pi (pi) . This booklet is ideal for young scientists and engineers to to acquaint them use of mathematical methods and applications.

The use of choice examples to show the practical application of matrix algebra and related mathematical tools in specific problems, it serves also as an introduction to linear programming, fluid mechanics, vector analysis and rf cicuit design.The full workings and code are made available for the use and adaptation of the reader. Here we walk through examples of using linear algebra and matrices to solve problems like cost estimation, we show how similar techniques are used in electrical theory and circuit design. We show how ballistics can predict the range of a football and the time of travel of a bullet. We see how we can generate 3d transforms of rotation and reflection of objects about general axes and mirrors. We look at the problem of signal rejection in transmission lines and give worked solutions.

This volume demonstrates the practical uses for a mathematical approach to science with evaluated examples. We examine the solution of pipe networks using both Hardy cross and Hazen Williams formulae. In chapter 2 we demonstrate how we can use a heuristic approach to the solution of stresses in motile structures. In chapter 3 we look at rocket science and work to a theoretical solution to how much fuel is needed to put an object into orbit.