Preface

A “transformation”, in its broadest sense, is an operator that relates two quantities. Its use permeates many every day artistic and scientific activities. An example of this would be its use in the manufacturing of tools to build and transform objects in different artistic expressions such as painting, sculpture, and theatre to determine the correct distance and size of things. In the scientific field, they are used in different disciplines such as Optics and Physics and more recently in Genomics and Bioinformatics. Due to the role transformations play in a broad spectrum of human creation, it is surprising to realize that few publications have been allocated to its study, not only in its mathematical context but also in its application to other disciplines. The reader will find in this book a study of this mathematical operator described by a large number of carefully selected examples, the reading and application, which can be easily understood without any rigorous mathematical knowledge. The first part introduces the affine transformations as mathematical operators, their properties, and their definition. The second part describes the differences between linear and nonlinear transformations. And the third part applies transformations in Acoustics, Actuary, Bioinformatics, Calculus, Cybernetics, Epidemiology, Genetics, Optics, Physics, Probability, and Vector Analysis. The author hopes the reader interested in Transformation theory finds useful the material presented here and that those who start studying this field, find this information motivating.