Vector calculusVector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Augustin-Louis CauchyBaron Augustin-Louis Cauchy (UKˈkoʊʃi,_ˈkaʊʃi , USkoʊˈʃiː , oɡystɛ̃ lwi koʃi; 21 August 1789 - 23 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors. He (nearly) single-handedly founded complex analysis and the study of permutation groups in abstract algebra.
Fractional calculusFractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator and of the integration operator and developing a calculus for such operators generalizing the classical one.
Integrable systemIn mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space.
ReasonReason is the capacity of applying logic consciously by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, language, mathematics, and art, and is normally considered to be a distinguishing ability possessed by humans. Reason is sometimes referred to as rationality. Reasoning is associated with the acts of thinking and cognition, and involves the use of one's intellect.
