Tensor calculus

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Calculus
Fundamental theorem Limits of functions Continuity Mean value theorem Rolle's theorem
Differential calculus Definitions Derivative Differential (infinitesimal) Differential of a function Generalizations of the derivative Concepts Notation for differentiation Second derivative Third derivative Change of variables Implicit differentiation Related rates Taylor's theorem Rules and identities Sums Products Chain rule Powers Quotients Faà di Bruno's formula
Integral calculus Lists of integrals Definitions Antiderivative Integral Improper integral Riemann integral Lebesgue integration Contour integral Integration by parts discs cylindrical shells substitution trigonometric substitution partial fractions changing order reduction formulae
Series Geometric Arithmetico-geometric Harmonic Alternating Power Binomial Taylor Convergence tests Summand limit (Term test) Ratio Root Integral Direct comparison Limit comparison Alternating series Cauchy condensation Dirichlet Abel
Vector calculus Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem Directional derivative
Multivariable calculus Formalisms Matrix Tensor Exterior Geometric Definitions Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian
Specialized calculi Calculus of variations Fractional Malliavin Stochastic
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In mathematics, tensor calculus or tensor analysis is an advanced extension of vector calculus to more general mathematical objects called tensor fields (tensors which change throughout space and with time).

Books

Dimitrienko, Yuriy (2002). Tensor Analysis and Nonlinear Tensor Functions. Kluwer Academic Publishers (Springer). ISBN 1-4020-1015-X.
J.R. Tyldesley (1973). An introduction to Tensor Analysis: For Engineers and Applied Scientists. Longman. ISBN 0-582-44355-5.
D.C. Kay (1988). Tensor Calculus. Schaum’s Outlines, McGraw Hill (USA). ISBN 0-07-033484-6.

Glossary of tensor theory

Scope

Mathematics	coordinate system multilinear algebra Euclidean geometry tensor algebra differential geometry exterior calculus tensor calculus

Physics Engineering	continuum mechanics electromagnetism transport phenomena general relativity computer vision

Notation

Tensor definitions

Related abstractions

Notable tensors

Mathematics	Kronecker delta Levi-Civita symbol metric tensor Christoffel symbols Ricci curvature Riemann curvature tensor Weyl tensor torsion tensor

Physics	moment of inertia angular momentum tensor spin tensor Cauchy stress tensor stress–energy tensor EM tensor gluon field strength tensor Einstein tensor metric (GR)

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