In this book Peta Trigger develops three methods of tackling problems in engineering science from first principles. The first two are matrix based, the required matrix and determinant properties being fully explained in the first two appendices. The third method is an iterative, approximation one. They are shown to be advantageous compared with other commonly used methods, and are applicable where the quantities involved are real or complex numbers. The text shows how the required equations for the application of each method are dervived, and a third appendix shows how matrices are set up for circuit parameters. Worked examples illustrating the application of each method are drawn from electronics and in each case the means of checking the result obtained for truth and accuracy is outlined. Readers are invited to test their understanding by completing a problem begun in the text using the method illustrated.