In mathematics, differential refers to several related notions[1] derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions.[2]
The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology.
Contents
1 Introduction
1.1 Basic notions
2 History and usage
3 Approaches
3.1 Naive approach
3.2 Differentials as linear maps
3.2.1 Differentials as linear maps on R
3.2.2 Differentials as linear maps on Rn
3.2.3 Differentials as linear maps on a vector space
3.3 Differentials as germs of functions
3.4 Algebraic geometry
3.4.1 Algebraic geometry notions
3.5 Synthetic differential geometry
3.6 Nonstandard analysis
4 Differential geometry
5 Other meanings
6 See also