Preface

 

        Who needs this book? Everybody who studies and uses the polynomial, exponential, logarithmic and power functions in any form. (Power functions are similar to polynomials but they have real powers). If you are mathematically inclined, you will be amazed to discover how closely these functions relate to each other and what interesting properties they have. If you work in any field that uses these functions in modeling of phenomena and approximating the behavior of processes, such as physical, chemical, social, economical – actually these functions are extremely popular workhorses in all areas that use at least the very basic mathematical modeling – you will find such things that will make your understanding of modeling and the models much, much better. Let us repeat: much, much better.

        The book provides tons of useful information and the whole conceptual framework for modeling of natural phenomena (to which the humans’ affairs, on a larger scale, belong too). We show by examples how the seemingly abstract mathematical concepts directly connect to the physical world and human societies; how to make the modeling adequate and meaningful, but not complicated. You will learn how to see the reality, the real and dynamic world behind the pure mathematical constructs and vice versa (which is absolutely essential for successful modeling of everything). We will freely travel from micro-micro world to Universe to explore the Nature’s arrangement based on relatively simple notions and mathematical apparatus. We will discover how Nature is governed by objective laws, how the Chaos and Order, the categories so respected by Ancient Greeks, interconnect to each other and exist in dynamic and eternal unity of their being, and how we can still objectively model the real world. Nature has no boundaries, which we, humans, are trying to impose on it all the time, apparently in order to facilitate our studies. However, when the Whole is broken into too many pieces, the meaning of the Whole is lost. This is why we have to be so careful dissecting the objects of our studies. So, be prepared to handle pieces but not loosing the sight of the Whole. This is not easy, this is what not so well studied and taught at schools, but this is the best and, in fact, the only way to cognize Nature and its inherently multifactor phenomena. This book uses namely this, the most efficient, but not the easiest, approach to study the subject. You will have to think when reading this book; we leave lots of room for doing this, in all dimensions and directions.

        Now, let us take a look at the specifics. These functions used to be considered as separate mathematical vehicles. In fact, their properties are tightly interconnected, we show this in the book. And so what, one can say. Well, the relationships are important in this world. If the university student discovers that his loving brother was taking last year the same courses he is going to take now, and the brother got A-plus in all of them, would it make any difference? We bet it would. Suppose, you know that the manufacturing industry and high-tech companies are leaving this country. Would you be confident in the brighter professional future of your son in this country if applied for mechanical engineering studies at the local university?

        Relationships are important in all areas, they allow to explain and anticipate many things, avoid lots of troubles, while gaining benefits. Why the students in commerce departments taught all the time: build networks, make connections. And they do! Maybe we should trust to instincts and experiences of business people? Business is close to real life, otherwise no business, do you agree?

        If we convince you that the relationships are important, then, how does one benefit from knowing the relationships between the aforementioned functions? This is easy. The short answer is this. We do not know a lot about each of these functions. However, if we know the relations between them, then all we know about all functions can be applied to one function. For instance, you do not know, how many solutions the exponential equation has. However, you know, how to find the number of solutions for the polynomials. Now, using the knowledge of relationships between these functions, you know how many solutions the exponential equation has. This is like knowing the Director of Analytics department in big company helps to find the job to your friend, the recent graduate. Life is interconnected, in all forms. Pretty good scientific thing to know as early as possible, if your dad forgot to tell you this. (For sure, he knows the trick, he was just too busy with this choppy life, do not blame him.)

 

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Last modified: 04/25/15