Schaum's Outline of Vector Analysis - Ebook Download

Author:            Spiegel; Murray Spiegel
Publisher:        MCGRAW-HILL
ISBN:               9780070602281
Publish date:  June 1968
Format:            PDF
Size:                 15 MB

Discription:

Introducing to students the vector analysis, this title presents different kinds of equations and natural aid for forming internal pictures of physical and geometrical thoughts. It is good for students of the physical sciences and of physics, mechanics, electromagnetic theory, aerodynamics, and many other fields.

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

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