Tensor calculus

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

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).

Tensor calculus has many real-life applications in physics and engineering, including stress analysis, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), and general relativity (see mathematics of general relativity).

See also

• Vector analysis
• Matrix calculus
• Tensors in curvilinear coordinates
• Multilinear subspace learning

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.