Field mathematics for electromagnetics, photonics, and materials science : a guide for the scientist and engineer / Bernard Maxum

Von:

Maxum, Bernard [aut]

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Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Tutorial texts in optical engineering ; 64Verlag: Bellingham, Wash. <1000 20th St. Bellingham WA 98225-6705 USA> : SPIE, c2005Beschreibung: 1 online resource (1 v. (various pagings) : ill.)ISBN:

9780819478689
0819455237
9780819455239

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Andere physische Formen: 0819455237. | 9780819455239. | Erscheint auch als: Kein Titel Druck-AusgabeDDC-Klassifikation:

620.00151563
620/.001/51563 22

LOC-Klassifikation:

TA330

DOI: DOI: 10.1117/3.581869Online-Ressourcen:

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Andere physische Formen: Also available in print version.Zusammenfassung: As electromagnetics, photonics, and materials science evolve, it is increasingly important for students and practitioners in the physical sciences and engineering to understand vector calculus and tensor analysis. This book provides a review of vector calculus. This review includes necessary excursions into tensor analysis intended as the reader's first exposure to tensors, making aspects of tensors understandable to advanced undergraduate students. This book will also prepare the reader for more advanced studies in vector calculus and tensor analysisZusammenfassung: Appendix A Vector Arithmetics and Applications -- Appendix B Vector Calculus in Orthogonal Coordinate Systems -- B.1 Cartesian Coordinate Geometry for the Divergence -- B.2 Cartesian Coordinate Geometry for the Curl -- B.3 Cylindrical Coordinate Geometry for the Divergence -- B.4 Summary of the Geometries for Divergence, Curl, and Gradient -- B.5 Orthogonal Coordinate System Parameters and Surface Graphics -- References --Zusammenfassung: Appendix C Intermediate Tensor Calculus in Support of Chapters 3 and 4 -- C.1 Explicit Standard Notation for General Rank Tensors -- C.2 Properties of First- and Second-Order Vector Differential Operators on Tensors -- C.3 Generalization of the Divergence Operator of Eq. (4.7-7) -- C.4 The Dual Nature of the Nabla Operator -- Reference --Zusammenfassung: Appendix D Coordinate Expansions of Vector Differential Operators -- D.1 Cartesian Coordinate Expansions -- D.2 Cylindrical Coordinate Expansions -- Glossary -- IndexZusammenfassung: Chapter 2 Vector Algebra Review -- 2.1 Variant and Invariant Scalars -- 2.2 Scalar Fields -- 2.3 Vector Fields -- 2.4 Arithmetic Vector Operations -- 2.5 Scalars, Vectors, Dyadics, and Tensors as Phasors -- 2.6 Vector Field Direction Lines -- 2.7 Scalar Field Equivalue Surfaces -- References --Zusammenfassung: Chapter 3 Elementary Tensor Analysis -- The tensor/dyadic issue -- 3.1 Directional Compoundedness, Rank, and Order of Tensors -- The rank/order issue -- 3.2 Tensor Components -- 3.3 Dyadics and the Unit Dyad -- 3.4 Dyadic Dot Products -- 3.5 The Four-Rank Elastic Modulus Tensor -- 3.6 The Use of Tensors in Nonlinear Optics -- 3.7 Term-by-Term Rank Consistency and the Rules for Determining the Rank after Performing Inner-Product Operations with Tensors -- 3.8 Summary of Tensors -- References --Zusammenfassung: Chapter 4 Vector Calculus Differential Forms With Excursions into Tensor Calculus -- 4.1 Introduction to Differential Operators and some Additional Tensor Rules -- 4.2 Scalar Differential Operators, Differential Equations, and Eigenvalues -- 4.3 The Gradient Differential Operator -- 4.4 The Divergence Differential Operator -- 4.5 The Curl Differential Operator -- 4.6 Tensorial Resultants of First-Order Vector Differential Operators -- 4.7 Second-Order Vector Differential Operators Differential Operators of Differential Operators -- References --Zusammenfassung: Chapter 5 Vector Calculus Integral Forms -- 5.1 Line Integrals of Vector (and Other Tensor) Fields -- 5.2 Surface Integrals of Vector (and Other Tensor) Fields -- 5.3 Gauss' (Divergence) Theorem -- 5.4 Stokes' (Curl) Theorem -- 5.5 Green's Mathematics -- References --Zusammenfassung: List of Figures -- List of Examples and Applications -- Acknowledgments -- Preface-- Chapter 1 Introduction -- 1.1 Notation -- 1.2 Spatial Differentials -- 1.3 Partial and Total Derivatives -- References --PPN: PPN: 1018189378Package identifier: Produktsigel: ZDB-50-SPI

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