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

Format:

Book

Author/Creator:

Maxum, Bernard, author.

Contributor:

Society of Photo-Optical Instrumentation Engineers.

Series:

Tutorial texts in optical engineering ; TT64.

Tutorial texts in optical engineering ; v. TT64

Language:

English

Subjects (All):

Vector analysis.

Engineering mathematics.

Physical Description:

1 online resource (1 volumes (various pagings) : illustrations, digital file.

Place of Publication:

Bellingham, Wash. : SPIE, [2005]

System Details:

Mode of access: World Wide Web.

text file

Summary:

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 analysis.

Contents:

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

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

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

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

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

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

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.

Notes:

"SPIE digital library."

Includes bibliographical references and index.

Title from PDF t.p. (viewed on August 22, 2009).

ISBN:

9780819478689

OCLC:

435912104

Access Restriction:

Restricted for use by site license.