Author: Spiegel; Murray SpiegelPublisher: MCGRAW-HILLISBN: 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
