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An Illustrative Guide to Multivariable and Vector Calculus

An Illustrative Guide to Multivariable and Vector Calculus

Stanley J. Miklavcic

Springer Nature Switzerland AG
2020
sidottu
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
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An Illustrative Guide to Multivariable and Vector Calculus

An Illustrative Guide to Multivariable and Vector Calculus

Stanley J. Miklavcic

Springer Nature Switzerland AG
2021
nidottu
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
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A Treatise on the Magnetic Vector Potential

A Treatise on the Magnetic Vector Potential

Kristján Óttar Klausen

Springer Nature Switzerland AG
2020
sidottu
The connection between the electric and magnetic fields is fundamental to our understanding of light as electromagnetic waves. The magnetic vector potential lies at the heart of this relation. The idea emerged in the early days of research in electromagnetism but was dismissed for more than half a century until the formulation of quantum electrodynamics. The magnetic vector potential is a pivotal concept with ties to many aspects of physics and mathematics. This book unravels the nature of the magnetic vector potential, highlights its connection to quantum mechanics and superconductivity, and explores the analogy with hydrodynamics.
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Optimal Control of Dynamic Systems Driven by Vector Measures

Optimal Control of Dynamic Systems Driven by Vector Measures

N. U. Ahmed; Shian Wang

Springer Nature Switzerland AG
2021
sidottu
This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions foroptimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
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Optimal Control of Dynamic Systems Driven by Vector Measures

Optimal Control of Dynamic Systems Driven by Vector Measures

N. U. Ahmed; Shian Wang

Springer Nature Switzerland AG
2022
nidottu
This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions foroptimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
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Narrow Operators on Function Spaces and Vector Lattices

Narrow Operators on Function Spaces and Vector Lattices

Mikhail Popov; Beata Randrianantoanina

De Gruyter
2012
sidottu
Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.
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Advances in Self-Organizing Maps and Learning Vector Quantization

Advances in Self-Organizing Maps and Learning Vector Quantization

Springer International Publishing AG
2014
nidottu
The book collects the scientific contributions presented at the 10th Workshop on Self-Organizing Maps (WSOM 2014) held at the University of Applied Sciences Mittweida, Mittweida (Germany, Saxony), on July 2–4, 2014. Starting with the first WSOM-workshop 1997 in Helsinki this workshop focuses on newest results in the field of supervised and unsupervised vector quantization like self-organizing maps for data mining and data classification.This 10th WSOM brought together more than 50 researchers, experts and practitioners in the beautiful small town Mittweida in Saxony (Germany) nearby the mountains Erzgebirge to discuss new developments in the field of unsupervised self-organizing vector quantization systems and learning vector quantization approaches for classification. The book contains the accepted papers of the workshop after a careful review process as well as summaries of the invited talks. Among these book chapters there are excellent examples of the use of self-organizing maps in agriculture, computer science, data visualization, health systems, economics, engineering, social sciences, text and image analysis and time series analysis. Other chapters present the latest theoretical work on self-organizing maps as well as learning vector quantization methods, such as relating those methods to classical statistical decision methods.All the contribution demonstrate that vector quantization methods cover a large range of application areas including data visualization of high-dimensional complex data, advanced decision making and classification or data clustering and data compression.
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Search for the Higgs Boson in the Vector Boson Fusion Channel at the ATLAS Detector

Search for the Higgs Boson in the Vector Boson Fusion Channel at the ATLAS Detector

Eric Ouellette

Springer International Publishing AG
2015
sidottu
This Thesis describes the first measurement of, and constraints on, Higgs boson production in the vector boson fusion mode, where the Higgs decays to b quarks (the most common decay channel), at the LHC. The vector boson fusion mode, in which the Higgs is produced simultaneously with a pair of quark jets, provides an unparalleled opportunity to study the detailed properties of the Higgs, including the possibility of parity and CP violation, as well as its couplings and mass. It thus opens up this new field of study for precision investigation as the LHC increases in energy and intensity, leading the way to this new and exciting arena of precision Higgs research.
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Advances in Self-Organizing Maps and Learning Vector Quantization

Advances in Self-Organizing Maps and Learning Vector Quantization

Springer International Publishing AG
2016
nidottu
This book contains the articles from the international conference 11th Workshop on Self-Organizing Maps 2016 (WSOM 2016), held at Rice University in Houston, Texas, 6-8 January 2016. WSOM is a biennial international conference series starting with WSOM'97 in Helsinki, Finland, under the guidance and direction of Professor Tuevo Kohonen (Emeritus Professor, Academy of Finland). WSOM brings together the state-of-the-art theory and applications in Competitive Learning Neural Networks: SOMs, LVQs and related paradigms of unsupervised and supervised vector quantization.The current proceedings present the expert body of knowledge of 93 authors from 15 countries in 31 peer reviewed contributions. It includes papers and abstracts from the WSOM 2016 invited speakers representing leading researchers in the theory and real-world applications of Self-Organizing Maps and Learning Vector Quantization: Professor Marie Cottrell (Universite Paris 1 Pantheon Sorbonne, France), Professor Pablo Estevez (University of Chile and Millennium Instituteof Astrophysics, Chile), and Professor Risto Miikkulainen (University of Texas at Austin, USA). The book comprises a diverse set of theoretical works on Self-Organizing Maps, Neural Gas, Learning Vector Quantization and related topics, and an excellent variety of applications to data visualization, clustering, classification, language processing, robotic control, planning, and to the analysis of astronomical data, brain images, clinical data, time series, and agricultural data.
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Search for the Higgs Boson in the Vector Boson Fusion Channel at the ATLAS Detector

Search for the Higgs Boson in the Vector Boson Fusion Channel at the ATLAS Detector

Eric Ouellette

Springer International Publishing AG
2016
nidottu
This Thesis describes the first measurement of, and constraints on, Higgs boson production in the vector boson fusion mode, where the Higgs decays to b quarks (the most common decay channel), at the LHC. The vector boson fusion mode, in which the Higgs is produced simultaneously with a pair of quark jets, provides an unparalleled opportunity to study the detailed properties of the Higgs, including the possibility of parity and CP violation, as well as its couplings and mass. It thus opens up this new field of study for precision investigation as the LHC increases in energy and intensity, leading the way to this new and exciting arena of precision Higgs research.
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Desingularization Strategies of Three-Dimensional Vector Fields

Desingularization Strategies of Three-Dimensional Vector Fields

Felipe Cano Torres

Springer-Verlag Berlin and Heidelberg GmbH Co. K
1987
nidottu
For a vector field #3, where Ai are series in X, the algebraic multiplicity measures the singularity at the origin. In this research monograph several strategies are given to make the algebraic multiplicity of a three-dimensional vector field decrease, by means of permissible blowing-ups of the ambient space, i.e. transformations of the type xi=x'ix1, 2"/I>i"/I>s, xi=x'i, i>s. A logarithmic point of view is taken, marking the exceptional divisor of each blowing-up and by considering only the vector fields which are tangent to this divisor, instead of the whole tangent sheaf. The first part of the book is devoted to the logarithmic background and to the permissible blowing-ups. The main part corresponds to the control of the algorithms for the desingularization strategies by means of numerical invariants inspired by Hironaka's characteristic polygon. Only basic knowledge of local algebra and algebraic geometry is assumed of the reader. The pathologies we find in the reduction of vector fields are analogous to pathologies in the problem of reduction of singularities in characteristic p. Hence the book is potentially interesting both in the context of resolution of singularities and in that of vector fields and dynamical systems.
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Recent Advances and Historical Development of Vector Optimization

Recent Advances and Historical Development of Vector Optimization

Springer-Verlag Berlin and Heidelberg GmbH Co. K
1987
nidottu
In vector optimization one investigates optimization problems in an abstract setting which have a not necessarily real-valued objective function. This scientific discipline is closely related to multi-objective optimization and multi-criteria decision making. This book contains refereed contributions to the "International Conference on Vector Optimization" held at the Technical University of Darmstadt from August 4-7, 1986. This meeting was an interdisciplinary forum devoted to new results in the theory, to applications as well as to the solution of vector optimization problems which are relevant in practice. Because of the great variety of topics covered by the contributions, the 25 articles of this volume are organized in different sections: Historical retrospect, mathematical theory, goal setting and decision making, engineering applications, and related topics. The papers of the invited State-of-the-Art Tutorials given by Professors J.M. Borwein, H. Eschenauer, W. Stadler and P.L. Yu are also included.
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Operator Algebras Generated by Commuting Projections: A Vector Measure Approach

Operator Algebras Generated by Commuting Projections: A Vector Measure Approach

Werner Ricker

Springer-Verlag Berlin and Heidelberg GmbH Co. K
1999
nidottu
This book presents a systematic investigation of the theory of those commutative, unital subalgebras (of bounded linear operators acting in a Banach space) which are closed for some given topology and are generated by a uniformly bounded Boolean algebra of projections. One of the main aims is to employ the methods of vector measures and integration as a unifying theme throughout. This yields proofs of several classical results which are quite different to the classical ones. This book is directed to both those wishing to learn this topic for the first time and to current experts in the field.
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