**Author: Spiegel; Murray SpiegelPublisher: MCGRAW-HILLISBN: 9780070602281Publish date: June 1968Format: PDFSize: 15 MB**

**Discription:**

This book introduces students to vector analysis, a concise way of presenting certain kinds of equations and a natural aid for forming mental pictures of physical and geometrical ideas. Students of the physical sciences and of physics, mechanics, electromagnetic theory, aerodynamics and a number of other fields will find this a rewarding and practical treatment of vector analysis. Key points are made memorable with the hundreds of problems with step-by-step solutions, and many review questions with answers.

Table of contents:

Vectors

Scalars

Vector algebra

Laws of vector algebra

Unit vectors

Rectangular unit vectors

Components of a vector

Scalar fields

Vector fields

The Dot and Cross Product 16 (19)

Dot or scalar products

Cross or vector products

Triple products Reciprocal sets of vectors

Vector Differentiation 35 (22)

Ordinary derivatives of vectors

Space curves

Continuity and differentiability

Differentiation formulas

Partial derivatives of vectors

Differentials of vectors

Differential geometry

Mechanics

Gradient, Divergence and Curl 57 (25)

The Vector differential operator del

Gradient

Divergence

Curl

Formulas involving del

Invariance

Vector Integration 82 (24)

Ordinary integrals of vectors

Line integrals

Surface integrals

Volume integrals

The Divergence Theorem, Stokes' Theorem, and 106(29)

Related Integral Theorems

The divergence theorem of Gauss

Stokes' theorem

Green's theorem in the plane

Related integral theorems

Integral operator form for del

Curvilinear Coordinates 135(31)

Transformation of coordinates

Orthogonal curvilinear coordinates

Unit vectors in curvilinear systems

Arc length and volume elements

Gradient, divergence and curl

Special orthogonal coordinate systems

Cylindrical coordinates

Spherical coordinates

Parabolic cylindrical coordinates

Paraboloidal coordinates

Elliptic cylindrical coordinates

Prolate spheroidal coordinates

Oblate spheroidal coordinates

Ellipsoidal coordinates

Bipolar coordinates

Tensor Analysis 166(52)

Physical laws, Spaces of N dimensions

Coordinate transformations

The summation convention

Contravariant and covariant vectors

Contravariant, Covariant and mixed tensors

The Kronecker delta

Tensors of rank greater than two

Scalars or invariants

Tensor fields

Symmetric and skew-symmetric tensors

Fundamental operations with tensors

Matrices

Matrix algebra

The line element and metric tensor

Conjugate or reciprocal tensors

Associated tensors

Length of a vector

Angle between vectors

Physical components

Christoffel's symbols

Transformation laws of Christoffel's symbols

Geodesics

Covariant derivatives

Permutation symbols and tensors

Tensor form of gradient, divergence and curl

The intrinsic or absolute derivative

Relative and absolute tensors

Index 218

**Download HERE in PDF format**

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