Perturbation Methods with Applications in Science and Engineering PDF Download

Author: Andreas J. Stylianides
Publisher: Springer
ISBN: 3319709968
Category : Education
Languages : en
Pages : 298

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Book Description
This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: • Theme 1: Epistemological issues related to proof and proving; • Theme 2: Classroom-based issues related to proof and proving; • Theme 3: Cognitive and curricular issues related to proof and proving; and • Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.

Author: Tommy Dreyfus
Publisher: Routledge
ISBN: 1351625403
Category : Education
Languages : en
Pages : 526

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Book Description
Developing Research in Mathematics Education is the first book in the series New Perspectives on Research in Mathematics Education, to be produced in association with the prestigious European Society for Research in Mathematics Education. This inaugural volume sets out broad advances in research in mathematics education which have accumulated over the last 20 years through the sustained exchange of ideas and collaboration between researchers in the field. An impressive range of contributors provide specifically European and complementary global perspectives on major areas of research in the field on topics that include: the content domains of arithmetic, geometry, algebra, statistics, and probability; the mathematical processes of proving and modeling; teaching and learning at specific age levels from early years to university; teacher education, teaching and classroom practices; special aspects of teaching and learning mathematics such as creativity, affect, diversity, technology and history; theoretical perspectives and comparative approaches in mathematics education research. This book is a fascinating compendium of state-of-the-art knowledge for all mathematics education researchers, graduate students, teacher educators and curriculum developers worldwide.

Author: Albert R. Baswell
Publisher:
ISBN: 9781634827423
Category : Electronic books
Languages : en
Pages : 206

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Book Description
Advances in Mathematics Research presents original studies on the leading edge of mathematics. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Topics discussed include using mathematical tessellation to model spherical particle packing structures; further results on fractional calculus for non-differentiable functions applications to z-transform and generalized functions; low earth orbit satellite constellations for local telecommunication and monitoring services; algorithm for autonomously calibrating reference flat of interferometer and residual influence of linear shift with two-flat method; dealing with non-significant interactions statuses between treatments by a suggested statistical approach; stochastic simultaneous perturbation as powerful method for state and parameter estimation in high dimensional systems; bounded trajectories of unstable piecewise linear systems and its applications; mathematical modeling for predicting battery lifetime through electrical models; and mathematical modeling of the lithium-ion battery lifetime using system identification theory.

Author: Gila Hanna
Publisher: Springer Science & Business Media
ISBN: 9400721293
Category : Education
Languages : en
Pages : 468

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Book Description
*THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

Author: Stephen Siklos
Publisher:
ISBN: 9781783747764
Category : Mathematics
Languages : en
Pages : 188

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Book Description
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Author: İlkay Bakırtaş
Publisher: BoD – Books on Demand
ISBN: 1789842557
Category : Mathematics
Languages : en
Pages : 170

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Book Description
The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.

Author: Albert R. Baswell
Publisher:
ISBN: 9781536197594
Category : Mathematics
Languages : en
Pages : 0

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Book Description
This compilation contains seven chapters, each detailing a particular advancement in mathematics research. Chapter One presents labeled paths as methods for encryption and decryption. Chapter Two presents the possibilities of risk assessment and management assistance built around Bayesian tools. Chapter Three analyzes in detail the Lie point symmetries of the second-order scalar ordinary differential equations appearing in the Painlevé-Gambier classification. Chapter Four focuses on the application of Adomian decomposition method (ADM) for solving singular and non-singular ordinary and partial differential equations with initial and boundary conditions. Chapter Five describes the structure of compact global attractor (Levinson center) for monotone Bohr/Levitan almost periodic dynamical systems. Chapter Six presents the mathematical modeling from the PI model of three real segments derived from the electric power network of two concessionaires located in the city of Ijuí, Brazil. Finally, Chapter Seven presents a study of the mathematical aspects of the theory of error-detecting/correcting codes based on coding theory.

Author: Fouzi Harrou
Publisher: BoD – Books on Demand
ISBN: 1838800913
Category : Technology & Engineering
Languages : en
Pages : 212

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Book Description
Fault detection, control, and forecasting have a vital role in renewable energy systems (Photovoltaics (PV) and wind turbines (WTs)) to improve their productivity, ef?ciency, and safety, and to avoid expensive maintenance. For instance, the main crucial and challenging issue in solar and wind energy production is the volatility of intermittent power generation due mainly to weather conditions. This fact usually limits the integration of PV systems and WTs into the power grid. Hence, accurately forecasting power generation in PV and WTs is of great importance for daily/hourly efficient management of power grid production, delivery, and storage, as well as for decision-making on the energy market. Also, accurate and prompt fault detection and diagnosis strategies are required to improve efficiencies of renewable energy systems, avoid the high cost of maintenance, and reduce risks of fire hazards, which could affect both personnel and installed equipment. This book intends to provide the reader with advanced statistical modeling, forecasting, and fault detection techniques in renewable energy systems.

Author: George Dantzig
Publisher: Princeton University Press
ISBN: 1400884179
Category : Mathematics
Languages : en
Pages : 651

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Book Description
In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948. Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems. Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.

Author: Vladimir Shikhman
Publisher: Springer Science & Business Media
ISBN: 1461418976
Category : Mathematics
Languages : en
Pages : 200

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Book Description
This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness. Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory. ​ ​