This book examines new approaches for the estimation of errors in approximate theories. Numerical and analytical methods in mechanics often require the establishment of a set of basic equations, and various approaches exist to create approximate theories from them. The problem is that nobody knows the boundaries of the estimation of errors in approximate theories. This book presents new approaches to overcome this problem and to provide the reader with suitable methods for the relevant field, including a representation of different scientific schools and different countries. These new methods are helping to solve many problems not only in analytical Mechanics but also in Physics, Mathematics, and Civil Engineering.
