Tensor Analysis on Manifolds

Author: Richard L. Bishop,Samuel I. Goldberg

Publisher: Courier Corporation

ISBN: 0486139239

Category: Mathematics

Page: 288

View: 2553

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DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
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Tensor Calculus

Author: J. L. Synge,A. Schild

Publisher: Courier Corporation

ISBN: 048614139X

Category: Mathematics

Page: 336

View: 4543

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Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.
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Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds

Author: Uwe Mühlich

Publisher: Springer

ISBN: 3319562649

Category: Technology & Engineering

Page: 125

View: 1757

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This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.
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Mathematical Physics

A Modern Introduction to Its Foundations

Author: Sadri Hassani

Publisher: Springer Science & Business Media

ISBN: 9780387985794

Category: Science

Page: 1026

View: 3294

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For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
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The Mathematics of Games

Author: John D. Beasley

Publisher: Courier Corporation

ISBN: 048615162X

Category: Mathematics

Page: 176

View: 4922

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Lucid, instructive, and full of surprises, this book examines how simple mathematical analysis can throw unexpected light on games of every type, from poker to golf to the Rubik's cube. 1989 edition.
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Curvature in Mathematics and Physics

Author: Shlomo Sternberg

Publisher: Courier Corporation

ISBN: 0486478556

Category: Mathematics

Page: 405

View: 6257

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As astronaut Donald K. Slayton notes in his Foreword, this chronicle emphasizes the cooperation of "humans on space and on the ground. It realistically balances the role of the highly visible astronaut with the mammoth supporting team." An official NASA publication, Suddenly, Tomorrow Came is profusely illustrated with forty-four figures and tables, plus sixty-three photographs. Historian Paul Dickson brings the narrative up to date with an informative new Introduction.
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Object Detection and Recognition in Digital Images

Theory and Practice

Author: Boguslaw Cyganek

Publisher: John Wiley & Sons

ISBN: 111861836X

Category: Science

Page: 552

View: 4491

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Object detection, tracking and recognition in images are key problems in computer vision. This book provides the reader with a balanced treatment between the theory and practice of selected methods in these areas to make the book accessible to a range of researchers, engineers, developers and postgraduate students working in computer vision and related fields. Key features: Explains the main theoretical ideas behind each method (which are augmented with a rigorous mathematical derivation of the formulas), their implementation (in C++) and demonstrated working in real applications. Places an emphasis on tensor and statistical based approaches within object detection and recognition. Provides an overview of image clustering and classification methods which includes subspace and kernel based processing, mean shift and Kalman filter, neural networks, and k-means methods. Contains numerous case study examples of mainly automotive applications. Includes a companion website hosting full C++ implementation, of topics presented in the book as a software library, and an accompanying manual to the software platform.
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The Absolute Differential Calculus (Calculus of Tensors)

Author: Tullio Levi-Civita

Publisher: Courier Corporation

ISBN: 0486316254

Category: Mathematics

Page: 452

View: 586

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Written by a distinguished mathematician, this classic examines the mathematical material necessary for a grasp of relativity theory. Covers introductory theories, fundamental quadratic forms, absolute differential calculus, and physical applications. 1926 edition.
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Tensors, Differential Forms, and Variational Principles

Author: David Lovelock,Hanno Rund

Publisher: Courier Corporation

ISBN: 048613198X

Category: Mathematics

Page: 400

View: 5007

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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
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An Introductory Course on Differentiable Manifolds

Author: Siavash Shahshahani

Publisher: Courier Dover Publications

ISBN: 0486820823

Category: Mathematics

Page: 368

View: 7680

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Based on author Siavash Shahshahani's extensive teaching experience, this volume presents a thorough, rigorous course on the theory of differentiable manifolds. Geared toward advanced undergraduates and graduate students in mathematics, the treatment's prerequisites include a strong background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstract algebra, and point set topology. More than 200 exercises offer students ample opportunity to gauge their skills and gain additional insights. The four-part treatment begins with a single chapter devoted to the tensor algebra of linear spaces and their mappings. Part II brings in neighboring points to explore integrating vector fields, Lie bracket, exterior derivative, and Lie derivative. Part III, involving manifolds and vector bundles, develops the main body of the course. The final chapter provides a glimpse into geometric structures by introducing connections on the tangent bundle as a tool to implant the second derivative and the derivative of vector fields on the base manifold. Relevant historical and philosophical asides enhance the mathematical text, and helpful Appendixes offer supplementary material.
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