ISBN: Ostalo
Godina izdanja: 1974
Jezik: Engleski
Oblast: Matematika
Autor: Strani

SV37
66055) Vector Analysis , Murray R. Spiegel ,
Schaum`s outline of theory and problems of vector analysis and an introduction to tensor analysis
by Spiegel, Murray R
Teorija i problemi vektorske analize i uvod u tenzorsku analizu
Publisher : McGraw-Hill New York 1974
Contents

1. VECTORS AND SCALARS.
Vectors. Scalars. Vector algebra. Laws of vector algebra. Unit vectors, Rectangular unit vectors. Components of a vector. Scalar fields. Vector fields.

2. THE DOT AND CROSS PRODUCT
Dot or scalar products. Cross or vector products. Triple products. Reciprocal sets of vectors.

3. VECTOR DIFFERENTIATION.
Ordinary derivatives of vectors. Space curves. Continuity and differentiability. Differen-tiation formulae. Partial derivatives of vectors. Differentials of vectors. Differential geometry. Mechanics.

4. GRADIENT, DIVERGENCE AND CURL..
The vector differential operator del. Gradient, Divergence. Curl. Formulae involving del. Invariance.

5. VECTOR INTEGRATION.
Ordinary integrals of vectors. Line integrals. Surface integrals. Volume integrals.

6. THE DIVERGENCE THEOREM, STOKES` THEOREM, AND RELATED INTEGRAL THEOREMS.
The divergence theorem of Gauss, Stokes theorem. Green`s theorem in the plane. Re-lated integral theorems. Integral operator form for del.

7. CURVILINEAR COORDINATES.
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.

8. TENSOR ANALYSIS.
Physical laws. Spaces of N dimensions. Coordinate transformations. The summatio convention. Contravariant and covariant vectors. Contravariant, covariant and mixe tensors. The Kronecker delta. Tensors of rank greater than two. Scalars or invariant Tensor fields. Symmetric and skew-symmetric tensors. Fundamental operations wit tensors. Matrices. Matrix algebra. The line element and metric tensor. Conjugate reciprocal tensors. Associated tensors. Length of a vector. Angle between vectors. Physic components. Christoffel`s symbols. Transformation laws of Christoffel`s symbols. Ge desics. Covariant derivatives. Permutation symbols and tensors. Tensor form of gradier divergence and curl. The intrinsic or absolute derivative. Relative and absolute tensors

INDEX.including 480 solved problems ; engleski jezik, mek povez, format 21 x 27,5 cm , 225 strana , nalepnica sa potpisom na naslovnoj strani ,