Shestopaloff proves new fundamental properties of sums of exponential functions and illustrates application of these properties to different kinds of natural phenomena, particularly applications in biology.

The book considers properties of polynomial, exponential, logarithmic and power functions. It introduces and proves important relationships between these functions, which enhances the theory and greatly improves the range of theoretical and practical applications, such as the modeling of physical, societal or economical processes. Relationship of the considered functions with the physical reality is another primarily subject of this book. Lots of illustrations and examples based on physical, biological, societal phenomena constitute a substantial part of the book, that facilitates the understanding of introduced modeling concepts and methods. The book is an excellent supplementary material for mathematical and physical courses for undergraduate and graduate studies; a valuable resource for mathematicians working in areas of algebra and analysis. Engineers, researchers, analysts, who use these functions in modeling of different processes and phenomena, will greatly benefit from this book.

The book considers system design in the entirety of all its interrelated factors. The focus is on conceptual, methodological and technological aspects. However, many other related issues are considered too, such as organization and structure of the development process, creation of development team and organization of its work. Each of these issues is covered in detail. The author presents an unbiased analysis of pros and cons of different approaches to system design, as well as his own conceptual vision of the discipline, a result of many years of software project development in high-tech and financial industries. The material is enhanced by examples, figures, diagrams and code excerpts. The content is accessible to a very wide audience. Even the unprepared reader can find a large part of the material useful and interesting, especially the conceptual content that can be easily transferred "across the border" to other disciplines. Specialists working in the software industry as well as those who teach or study related subjects in an academic environment will find this book highly informative and thought provoking. It is especially recommended for system designers, advanced level programmers, engineers, project leaders and managers.

This book presents a coherent and comprehensive coverage of mathematical foundations for mortgages and annuities, as well as related computational algorithms for software applications and financial calculators. It also considers the specifics of implementing these algorithms in industrial financial systems. Starting from scratch, the reader, together with the author, builds a solid, efficient and complete knowledge base. Concise and carefully arranged material presents equally well all necessary theoretical underpinnings of the subject and its practical aspects. Lots of numerical examples, exercises and problems contribute to producing a high quality text. Undergraduate and graduate students in a variety of disciplines, from financial mathematics to investments to computer science, as well as teachers, professors, and industry specialists will find this book an invaluable educational and practical resource.

This book studies the role of physical mechanisms in the growth and replication of living organisms. Presently, these phenomena are overwhelmingly considered as biological, genetic, and biochemical ones, which is much true. However, natural phenomena exist in a real world that does not have purely physical or biological boundaries, which subjectively imposed by excessive human desire for classification and clustering of everything. Physical laws influence such universal phenomena as growth and replication too. The book presents an interesting hypothesis, and its convincing proofs, with regard to existence of such fundamental physical mechanisms shaping the organisms¿ growth and replication. It introduces a mathematical growth equation illustrated by numerical examples. The material is presented in such a way that it is accessible to any person interested in the subject.

The author proposes a special nonlinear quantum field theory. In a linear approximation, this theory can be presented in the form of the Standard Model (SM) theory. The richer physical structure of this nonlinear theory makes it possible to exceed the limits of SM and remove its known incompleteness. We show that nonlinearity of the field is critical for the appearance of charges and masses of elementary particles, for confinement of quarks, and many other effects, whose description within the framework of SM causes difficulties. In this case, the mechanism of generation of masses is mathematically similar to Higgs's mechanism, but it is considerably simpler and does not include the additional particles. The proposed theory does not examine the theory of gravity, but reveals the mathematical similarity of the nonlinear field equations of both theories. The book is intended for undergraduate and graduate students studying the theory of elementary particles, as well as for specialists working in this field.

One may argue that life is not so simple. From Shestopaloff' s perspective, it exactly is. What he successfully did in the discussed work is logical holistic arrangement of physical and biological puzzles to reveal the landscape of Living Nature more informative than mixed up pieces. Reviewed book is well written reading-matter for all people interesting in physical basis of life, without rich mathematical experience. It is also carrying some dose of philosophical reflections about science as it. It may be recommended as valuable lecture especially for students and scientists working in the area of biology and biophysics

This second edition provides a broad range of methods and concepts required for the analysis and solution of equations which arise in the modeling of phenomena in the natural, engineering, and applied mathematical sciences. It may be used productively by both undergraduate and graduate students, as well as others who wish to learn, understand, and apply these techniques. Detailed discussions are also given for several topics that are not usually included in standard textbooks at this level of presentation: qualitative methods for differential equations, dimensionalization and scaling, elements of asymptotics, difference equations and several perturbation procedures. Further, this second edition includes several new topics covering functional equations, the Lambert-W function, nonstandard sets of periodic functions, and the method of dominant balance. Each chapter contains a large number of worked examples and provides references to the appropriate books and literature.