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CITATION

Spiegel, Murray and Lipschutz, Seymour. Schaum's Outline of Vector Analysis, 2ed. US: McGraw-Hill, 2009.

Schaum's Outline of Vector Analysis, 2ed

Authors: Murray Spiegel and Seymour Lipschutz

Published:  April 2009

eISBN: 9780071815222 0071815228 | ISBN: 9780071615457
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  • Contents
  • Chapter 1 Vectors and Scalars
  • 1.1 Introduction
  • 1.2 Vector Algebra
  • 1.3 Unit Vectors
  • 1.4 Rectangular Unit Vectors i, j, k
  • 1.5 Linear Dependence and Linear Independence
  • 1.6 Scalar Field
  • 1.7 Vector Field
  • 1.8 Vector Space R[Sup(n)]
  • Chapter 2 The Dot and Cross Product
  • 2.1 Introduction
  • 2.2 Dot or Scalar Product
  • 2.3 Cross Product
  • 2.4 Triple Products
  • 2.5 Reciprocal Sets of Vectors
  • Chapter 3 Vector Differentiation
  • 3.1 Introduction
  • 3.2 Ordinary Derivatives of Vector-Valued Functions
  • 3.3 Continuity and Differentiability
  • 3.4 Partial Derivative of Vectors
  • 3.5 Differential Geometry
  • Chapter 4 Gradient, Divergence, Curl
  • 4.1 Introduction
  • 4.2 Gradient
  • 4.3 Divergence
  • 4.4 Curl
  • 4.5 Formulas Involving ▽
  • 4.6 Invariance
  • Chapter 5 Vector Integration
  • 5.1 Introduction
  • 5.2 Ordinary Integrals of Vector Valued Functions
  • 5.3 Line Integrals
  • 5.4 Surface Integrals
  • 5.5 Volume Integrals
  • Chapter 6 Divergence Theorem, Stokes’ Theorem, and Related Integral Theorems
  • 6.1 Introduction
  • 6.2 Main Theorems
  • 6.3 Related Integral Theorems
  • Chapter 7 Curvilinear Coordinates
  • 7.1 Introduction
  • 7.2 Transformation of Coordinates
  • 7.3 Orthogonal Curvilinear Coordinates
  • 7.4 Unit Vectors in Curvilinear Systems
  • 7.5 Arc Length and Volume Elements
  • 7.6 Gradient, Divergence, Curl
  • 7.7 Special Orthogonal Coordinate Systems
  • Chapter 8 Tensor Analysis
  • 8.1 Introduction
  • 8.2 Spaces of N Dimensions
  • 8.3 Coordinate Transformations
  • 8.4 Contravariant and Covariant Vectors
  • 8.5 Contravariant, Covariant, and Mixed Tensors
  • 8.6 Tensors of Rank Greater Than Two, Tensor Fields
  • 8.7 Fundamental Operations with Tensors
  • 8.8 Matrices
  • 8.9 Line Element and Metric Tensor
  • 8.10 Associated Tensors
  • 8.11 Christoffel’s Symbols
  • 8.12 Length of a Vector, Angle between Vectors, Geodesics
  • 8.13 Covariant Derivative
  • 8.14 Permutation Symbols and Tensors
  • 8.15 Tensor Form of Gradient, Divergence, and Curl
  • 8.16 Intrinsic or Absolute Derivative
  • 8.17 Relative and Absolute Tensors
  • Index