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Applied Mathematics

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ISBN: 9781789239058 9781789239065 9781839622229 Year: Pages: 158 DOI: 10.5772/intechopen.78131 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:53

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This book contains well-written monographs within the broad spectrum of applied mathematics, offering an interesting reading of some of the current trends and problems in this fascinating and critically important field of science to a broad category of researchers and practitioners. Recent developments in high-performance computing are radically changing the way we do numerics. As the size of problems is expected to grow very large in the future, the gap between fast and slow algorithms is growing rapidly. Novel classes of numerical methods with reduced computational complexity are therefore needed to make the rigorous numerical solution of difficult problems arising in an industrial setting more affordable. The book is structured in four distinct parts, according to the purpose and approaches used in the development of the contributions, ranging from optimization techniques to graph-oriented approaches and approximation theory, providing a good mix of both theory and practice.

Handbook of Contact Mechanics

Authors: --- ---
ISBN: 9783662587096 Year: Pages: 347 DOI: 10.1007/978-3-662-58709-6 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Agriculture (General)
Added to DOAB on : 2020-01-29 11:21:06
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This open access book contains a structured collection of the complete solutions of all essential axisymmetric contact problems. Based on a systematic distinction regarding the type of contact, the regime of friction and the contact geometry, a multitude of technically relevant contact problems from mechanical engineering, the automotive industry and medical engineering are discussed. In addition to contact problems between isotropic elastic and viscoelastic media, contact problems between transversal-isotropic elastic materials and functionally graded materials are addressed, too. The optimization of the latter is a focus of current research especially in the fields of actuator technology and biomechanics. The book takes into account adhesive effects which allow access to contact-mechanical questions about micro- and nano-electromechanical systems. Solutions of the contact problems include both the relationships between the macroscopic force, displacement and contact length, as well as the stress and displacement fields at the surface and, if appropriate, within the half-space medium. Solutions are always obtained with the simplest available method - usually with the method of dimensionality reduction (MDR) or approaches which use the solution of the non-adhesive normal contact problem to solve the respective contact problem.

The Legacy of Felix Klein

Authors: --- --- --- --- et al.
Book Series: ICME-13 Monographs ISBN: 9783319993867 Year: Pages: 226 DOI: 10.1007/978-3-319-99386-7 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2020-02-04 11:21:05
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This open access book provides an overview of Felix Klein’s ideas, highlighting developments in university teaching and school mathematics related to Klein’s thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein’s ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein’s ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint.

Polynomials - Theory and Application

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ISBN: 9781838802691 9781838802707 9781838806392 Year: Pages: 172 DOI: 10.5772/intechopen.79093 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:53

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Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.

Fractal Analysis

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ISBN: 9781789854336 9781789854343 Year: Pages: 112 DOI: 10.5772/intechopen.74876 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:53

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The aim of this book is to show some applications of fractal analysis in the fields of sciences. The first chapter introduces the readers to the book, while the second chapter shows the methods and challenges of fractal analysis of time-series data sets. The third chapter demonstrates fractal geometry as an attractive choice for miniaturized planar microwave filter design. The fourth chapter presents fractal antennas for wearable applications. The objective of the fifth chapter is to show some Parrondian games in discrete dynamic systems, while the last chapter reveals fractal structures of carbon nanotube system arrays.

European Traditions in Didactics of Mathematics

Authors: --- --- --- --- et al.
Book Series: ICME-13 Monographs ISBN: 9783030055141 Year: Pages: 212 DOI: 10.1007/978-3-030-05514-1 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2020-02-04 11:21:05
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This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states. It shows that while they all share common features both in the practice of learning and teaching at school and in research and development, they each have special features due to specific historical and cultural developments. The book also presents interesting historical facts about these didactic traditions, the theories and examples developed in these countries.

Manifolds II - Theory and Applications

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ISBN: 9781838803094 9781838803100 9781838807160 Year: Pages: 146 DOI: 10.5772/intechopen.75217 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:53

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Differential geometry is a very active field of research and has many applications to areas such as physics, in particular gravity. The chapters in this book cover a number of subjects that will be of interest to workers in these areas. It is hoped that these chapters will be able to provide a useful resource for researchers with regard to current fields of research in this important area.

Values and Valuing in Mathematics Education

Authors: --- ---
Book Series: ICME-13 Monographs ISBN: 9783030168926 Year: Pages: 222 DOI: 10.1007/978-3-030-16892-6 Language: English
Publisher: Springer Nature
Subject: Education
Added to DOAB on : 2020-02-04 11:21:05
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This engaging open access book discusses how a values and valuing perspective can facilitate a more effective mathematics pedagogical experience, and allows readers to explore multiple applications of the values perspective across different education systems. It also clearly shows that teaching mathematics involves not only reasoning and feelings, but also students’ interactions with their cultural setting and each other. The book brings together the work of world leaders and new thinkers in mathematics educational research to improve the learning and teaching of mathematics. Addressing themes such as discovering hidden cultural values, a multicultural society and methodological issues in the investigation of values in mathematics, it stimulates readers to consider these topics in cross-cultural ways, and offers suggestions for research and classroom practice. It is a valuable resource for scholars of mathematics education, from early childhood through to higher education and an inspiring read for all mathematics teachers. ; Features the intellectual work of researchers from different ethnicities and nationalities Offers an alternative perspective of complementing cognition and affect Presents a comprehensive collection of values and valuing in mathematics education

Lines of Inquiry in Mathematical Modelling Research in Education

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Book Series: ICME-13 Monographs ISBN: 9783030149314 Year: Pages: 259 DOI: 10.1007/978-3-030-14931-4 Language: English
Publisher: Springer Nature
Subject: Education
Added to DOAB on : 2020-02-04 11:21:05
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This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators

The Essence of Mathematics Through Elementary Problems

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Book Series: OBP Series in Mathematics ISSN: 2397-1126/2397-1134 ISBN: 9781783746996 9781783747016 Year: DOI: https://doi.org/10.11647/OBP.0168 Language: English
Publisher: Open Book Publishers
Subject: Mathematics
Added to DOAB on : 2019-06-25 18:14:54
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"It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works."

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