Tensor Calculus"This book is an excellent classroom text, since it is clearly written, contains numerous problems and exercises, and at the end of each chapter has a summary of the significant results of the chapter." — Quarterly of Applied Mathematics. Fundamental introduction for beginning student of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, special types of space, relative tensors, ideas of volume, and more. |
Contents
I | 3 |
II | 6 |
III | 9 |
IV | 12 |
V | 15 |
VI | 18 |
VII | 20 |
VIII | 26 |
XXIV | 142 |
XXVI | 149 |
XXVII | 156 |
XXVIII | 162 |
XXIX | 168 |
XXX | 190 |
XXXI | 202 |
XXXII | 213 |
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Common terms and phrases
absolute derivative arbitrary C₁ Cartesian coordinates Cartesian tensor cell Christoffel symbols coefficients configuration-space Consider constant curvature contravariant vector coordinate system covariant derivative covariant tensor covariant vector curvature tensor curve curvilinear coordinates defined definition denote differential equations ds² dx¹ dx² equations of motion Euclidean 3-space Exercise expression flat space fluid follows formulae geometry given Green's theorem Hence homogeneous coordinates infinitesimal displacement integral Jacobian Kronecker delta line element M-cell Maxwell's equations metric form metric tensor normal notation obtain orthogonal parallel propagation parameter parametric lines particle permutation symbols physical components plane Prove rectangular Cartesian coordinates relative tensor Riemannian space rigid body satisfied second order set of quantities Show skew-symmetric sphere suffixes surface tensor calculus tensor character theorem trajectory transformation unit vector V₁ V₂ values vanishes vector field write zero δι მე