Functional linguisticsFunctional linguistics is an approach to the study of language characterized by taking systematically into account the speaker's and the hearer's side, and the communicative needs of the speaker and of the given language community. Linguistic functionalism spawned in the 1920s to 1930s from Ferdinand de Saussure's systematic structuralist approach to language (1916). Functionalism sees functionality of language and its elements to be the key to understanding linguistic processes and structures.
Systemic functional linguisticsSystemic functional linguistics (SFL) is an approach to linguistics, among functional linguistics, that considers language as a social semiotic system. It was devised by Michael Halliday, who took the notion of system from J. R. Firth, his teacher (Halliday, 1961). Firth proposed that systems refer to possibilities subordinated to structure; Halliday "liberated" choice from structure and made it the central organising dimension of SFL.
Differentiable manifoldIn mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts, since each chart lies within a vector space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart.
Differential formIn mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression f(x) dx is an example of a 1-form, and can be integrated over an interval [a, b] contained in the domain of f: Similarly, the expression f(x, y, z) dx ∧ dy + g(x, y, z) dz ∧ dx + h(x, y, z) dy ∧ dz is a 2-form that can be integrated over a surface S: The symbol ∧ denotes the exterior product, sometimes called the wedge product, of two differential forms.
