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An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ?elds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail. A useful tool for any

Vector fields. --- Geometry, Differential. --- Differential geometry --- Direction fields (Mathematics) --- Fields, Direction (Mathematics) --- Fields, Slope (Mathematics) --- Fields, Vector --- Slope fields (Mathematics) --- Vector analysis

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The aim of this book is to facilitate the use of Stokes' Theorem in applications.  The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables.  Several practical methods and many solved exercises are provided. This book tries to show that vector analysis and vector calculus are not always at odds with one another.   Key topics include: -vectors and vector fields; -line integrals; -regular k-surfaces; -flux of a vector field; -orientation of a surface; -differential forms; -Stokes' theorem; -divergence theorem.   This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables.  The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.

Calculus of variations. --- Stokes' theorem. --- Vector analysis. --- Vector analysis --- Stokes' theorem --- Calculus of variations --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Operations Research --- Geometry --- Isoperimetrical problems --- Variations, Calculus of --- Mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Mathematical physics. --- Differential geometry. --- Global Analysis and Analysis on Manifolds. --- Differential Geometry. --- Mathematical Applications in the Physical Sciences. --- Differential geometry --- Physical mathematics --- Physics --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Maxima and minima --- Integrals --- Vector valued functions --- Algebra, Universal --- Numbers, Complex --- Quaternions --- Spinor analysis --- Vector algebra --- Global analysis. --- Global differential geometry. --- Global analysis (Mathematics) --- Manifolds (Mathematics) --- Geometry, Differential.

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This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts.  The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.

Functional analysis. --- Inner product spaces. --- Mathematical optimization. --- Mathematics. --- Normed linear spaces. --- Normed linear spaces --- Functional analysis --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Linear normed spaces --- Normed vector spaces --- Functional calculus --- Functional Analysis. --- Optimization. --- Calculus of variations --- Functional equations --- Integral equations --- Banach spaces --- Vector analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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This textbook is a strong addition to existing introductory literature on algebraic geometry. The author’s treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields. Unique features of this textbook: - Contains a rapid introduction to complex algebraic geometry - Includes background material on topology, manifold theory and sheaf theory - Analytic and algebraic approaches are developed somewhat in parallel The presentation is easy going, elementary, and well illustrated with examples. “Algebraic Geometry over the Complex Numbers” is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory.

Geometry, Algebraic. --- Numbers, Complex. --- Geometry, Algebraic --- Numbers, Complex --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Algebraic geometry --- Complex numbers --- Imaginary quantities --- Quantities, Imaginary --- Mathematics. --- Algebraic geometry. --- Functions of complex variables. --- Topology. --- Algebraic Geometry. --- Several Complex Variables and Analytic Spaces. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Algebra, Universal --- Quaternions --- Vector analysis --- Geometry, algebraic. --- Differential equations, partial. --- Partial differential equations

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This book is the second enlarged and revised edition of the first successful monograph on complex-valued neural networks (CVNNs) published in 2006, which lends itself to graduate and undergraduate courses in electrical engineering, informatics, control engineering, mechanics, robotics, bioengineering, and other relevant fields. In the second edition the recent trends in CVNNs research are included, resulting in e.g. almost a doubled number of references. The parametron invented in 1954 is also referred to with discussion on analogy and disparity. Also various additional arguments on the advantages of the complex-valued neural networks enhancing the difference to real-valued neural networks are given in various sections. The book is useful for those beginning their studies, for instance, in adaptive signal processing for highly functional sensing and imaging, control in unknown and changing environment, robotics inspired by human neural systems, and brain-like information processing, as well as interdisciplinary studies to realize comfortable society. It is also helpful to those who carry out research and development regarding new products and services at companies. The author wrote this book hoping in particular that it provides the readers with meaningful hints to make good use of neural networks in fully practical applications. The book emphasizes basic ideas and ways of thinking. Why do we need to consider neural networks that deal with complex numbers? What advantages do the complex-valued neural networks have? What is the origin of the advantages? In what areas do they develop principal applications? This book answers these questions by describing details and examples, which will inspire the readers with new ideas.    .

Neural networks (Computer science) --- Numbers, Complex --- Engineering & Applied Sciences --- Computer Science --- Numbers, Complex. --- Complex numbers --- Imaginary quantities --- Quantities, Imaginary --- Artificial neural networks --- Nets, Neural (Computer science) --- Networks, Neural (Computer science) --- Neural nets (Computer science) --- Engineering. --- Artificial intelligence. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Algebra, Universal --- Quaternions --- Vector analysis --- Natural computation --- Artificial Intelligence.