Vector and tensor analysis

Vector and Tensor Analysis [Young]......Page Vector_Analysis_0001.djvu
Title......Page Eutiquio C. Young. Vector and Tensor Analysis (Pure & Applied Mathematics) (Marcel Dekker Ltd,1993)(ISBN 0824787897)(511s).djvu
Copyright......Page 0002.djvu
Preface to the Second Edition......Page 0003.djvu
Preface to the First Edition......Page 0004.djvu
Contents......Page 0006.djvu
1.1 Introduction......Page 0009.djvu
1.2 Definition of a vector......Page 0010.djvu
1.3 Geometric representation of a vector......Page 0013.djvu
1.4 Addition and scalar multiplication......Page 0019.djvu
1.5 Some applications in geometry......Page 0032.djvu
1.6 Scalar product......Page 0036.djvu
1.7 Vector product......Page 0045.djvu
1.8 Lines and planes in space......Page 0061.djvu
1.9 Scalar and vector triple products......Page 0073.djvu
2.1 Vector functions of a real variable......Page 0082.djvu
2.2 Algebra of vector functions......Page 0084.djvu
2.3 Limit, continuity, and derivatives......Page 0087.djvu
2.4 Space curves and tangent vectors......Page 0094.djvu
2.5 Arc length as a parameter......Page 0103.djvu
2.6 Simple geometry of curves......Page 0109.djvu
2.7 Torsion and Frenet-Serret formulas......Page 0120.djvu
2.8 Applications to curvilinear motions......Page 0125.djvu
2.9 Curvilinear motion in polar coordinates......Page 0135.djvu
2.10 Cylindrical and spherical coordinates......Page 0144.djvu
3.1 Scalar and vector fields......Page 0154.djvu
3.2 Algebra of vector fields......Page 0157.djvu
3.3 Directional derivative of a scalar field......Page 0161.djvu
3.4 Gradient of a scalar field......Page 0167.djvu
3.5 Divergence of a vector field......Page 0175.djvu
3.6 Curl of a vector field......Page 0183.djvu
3.7 Other properties of the divergence and the curl......Page 0188.djvu
3.8 Curvilinear coordinate systems......Page 0192.djvu
3.9 Gradient, divergence and curl in orthogonal curvilinear coordinate systems......Page 22071_to_0300aae.tif.djvu
4. Integral Calculus of Scalar and Vector Fields......Page 22071_to_0300aan.tif.djvu
4.1 Line integrals of scalar fields......Page 22071_to_0300aao.tif.djvu
4.2 Line integrals of vector fields......Page 22071_to_0300aba.tif.djvu
4.3 Properties of line integrals......Page 22071_to_0300abh.tif.djvu
4.4 Line integrals independent of path......Page 22071_to_0300abp.tif.djvu
4.5 Green\'s theorem in the plane......Page 22071_to_0300aca.tif.djvu
4.6 Parametric representation of surfaces......Page 22071_to_0300ack.tif.djvu
4.7 Surface area......Page 22071_to_0300acs.tif.djvu
4.8 Surface integrals......Page 22071_to_0300ada.tif.djvu
4.9 The divergence (Gauss\') theorem......Page 22071_to_0300adl.tif.djvu
4.10 Applications of the divergence theorem......Page 22071_to_0300adp.tif.djvu
4.11 Stokes\' theorem......Page 0303.djvu
4.12 Some applications of Stokes\' theorem......Page 0308.djvu
5.1 Introduction......Page 0314.djvu
5.2 Notation and summation convention......Page 0315.djvu
5.3 Transformations of rectangular Cartesian coordinate systems......Page 0318.djvu
5.4 Transformation law for vectors......Page 0327.djvu
5.5 Cartesian tensors......Page 0334.djvu
5.6 Stress tensor......Page 0341.djvu
5.7 Algebra of Cartesian tensors......Page 0352.djvu
5.8 Principal axes of second order tensors......Page 0359.djvu
5.9 Differentiation of Cartesian tensor fields......Page 0368.djvu
5.10 Strain tensor......Page 0372.djvu
6.1 Oblique Cartesian coordinates......Page 0380.djvu
6.2 Reciprocal basis; transformations of oblique coordinate systems......Page 0384.djvu
6.3 Tensors in oblique Cartesian coordinate systems......Page 0394.djvu
6.4 Algebra of tensors in oblique coordinates......Page 22071_to_0500aad.tif.djvu
6.5 The metric tensor......Page 22071_to_0500aaj.tif.djvu
6.6 Transformations of curvilinear coordinates......Page 22071_to_0500aat.tif.djvu
6.7 General tensors......Page 22071_to_0500abc.tif.djvu
6.8 Covariant derivative of a vector......Page 22071_to_0500abm.tif.djvu
6.9 Transformation of Christoffel symbols......Page 22071_to_0500abt.tif.djvu
6.10 Covariant derivative of tensors......Page 22071_to_0500aca.tif.djvu
6.11 Gradient, divergence, Laplacian, and curl in general coordinates......Page 22071_to_0500ace.tif.djvu
6.12 Equations of motion of a particle......Page 22071_to_0500acm.tif.djvu
Solutions to Selected Problems......Page 22071_to_0500acw.tif.djvu
Index......Page 22071_to_0511aaa.tif.djvu