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                <text>A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why researchers and practitioners utilize iterative procedures from which a sequence is being generated approximating the solution under some conditions on the initial data. This type of research is considered most interesting and challenging. This is our motivation for the introduction of this special issue on Iterative Procedures.</text>
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                <text>This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. </text>
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                <text> Petráš, Ivo</text>
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                <text>Numerical methods are designed to approximate one thing or another. Sometimes roots, sometimes derivatives or definite integrals, or curves, or solutions of differential equations. As numerical methods produce only approximations to these things, it is important to have some idea how accurate they are. Sometimes accuracy comes down to careful algebraic analysis—sometimes careful analysis of the calculus, and often careful analysis of Taylor polynomials. But before we can tackle those details, we should discuss just how error and, therefore, accuracy are measured. There are two basic measurements of accuracy: absolute error and relative error. Suppose that p is the value we are approximating, and p˜ is an approximation of p. Then p˜ misses the mark by exactly the quantity p˜− p, the so-called error. Of course, p˜ − p will be negative when p˜ misses low. That is, when the approximation p˜ is less than the exact value p. On the other hand, p˜ − p will be positive when p˜ misses high. But generally, we are not concerned with whether our approximation is too high or too low. We just want to know how far off it is. Thus, we most often talk about the absolute error, |p˜ − p|. You might recognize the expression |p˜ − p| as the distance between p˜ and p, and that’s not a bad way to think about absolute error.</text>
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                <text>Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present. This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. </text>
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&#13;
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&#13;
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                <text> This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired.&#13;
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                <text> All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.&#13;
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                <text>This book originated from my class notes for teaching Math 286 at the University of Illinois at Urbana-Champaign in Fall 2008 and Spring 2009. It is a ﬁrst course on differential equations for&#13;
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                <text>Much of the material of Chapters 2-6 and 8 has been adapted from thewidely used textbook “Elementary differential equations and boundary value problems” by Boyce &amp; DiPrima (John Wiley &amp; Sons, Inc., Seventh Edition, ○c 2001). Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven H. Strogatz (Perseus Publishing, ○c 1994)</text>
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                <text>Combinatorics is a subfield of "discrete mathematics," so we should begin by asking what discrete mathematics means. The differences are to some extent a matter of opinion, and various mathematicians might classify specific topics differently.&#13;
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                <text> &#13;
There’s an ancient view, still widely held, that what makes human beings special—what distinguishes us from the “beasts of the field”—is that we are rational. What does rationality consist in? That’s a vexed question, but one possible response goes roughly like this: we manifest&#13;
our rationality by engaging in activities that involve reasoning—making claims and backing them up with reasons, acting in accord with reasons and beliefs, drawing inferences from available evidence, and so on.&#13;
This reasoning activity can be done well and it can be done badly—it can be done correctly or&#13;
incorrectly. Logic is the discipline that aims to distinguish good reasoning from bad. Since reasoning is central to all fields of study—indeed, since it’s arguably central to being&#13;
human—the tools developed in logic are universally applicable. Anyone can benefit from studying&#13;
logic by becoming a more self-aware, skillful reasoner. &#13;
This covers a variety of topics at an introductory level. Chapter One introduces basic notions, such as arguments and explanations, validity and soundness, deductive and inductive reasoning; it also covers basic analytical techniques, such as distinguishing premises from conclusions and diagramming arguments. Chapter Two discusses informal logical fallacies. Chapters Three and&#13;
Four concern deductive logic, introducing the basics of Aristotelian and Sentential Logic, respectively. Chapters Five and Six concern inductive logic. Chapter Five deals with analogical and causal reasoning, including a discussion of Mill’s Methods. Chapter Six covers basic&#13;
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