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

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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 excursi...

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Bibliographic Details
Main Author: Maxum, Bernard
Corporate Author: Society of Photo-optical Instrumentation Engineers
Format: eBook
Language:English
Published: Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA) : SPIE, [2005]
Series:SPIE tutorial texts ; TT64.
Subjects:
Engineering mathematics.
Vector analysis.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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
  • 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
  • Appendix D Coordinate Expansions of Vector Differential Operators
  • D.1 Cartesian Coordinate Expansions
  • D.2 Cylindrical Coordinate Expansions
  • Glossary
  • Index.
  • 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
  • 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
  • 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
  • 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
  • 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