ApproximationAn approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus, from proximus meaning very near and the prefix ad- (ad- before p becomes ap- by assimilation) meaning to. Words like approximate, approximately and approximation are used especially in technical or scientific contexts. In everyday English, words such as roughly or around are used with a similar meaning. It is often found abbreviated as approx.
Finite groupIn abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose in the 19th century.
Meshfree methodsIn the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort.
Linear approximationIn mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations. Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case states that where is the remainder term.
Spectral methodSpectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and then to choose the coefficients in the sum in order to satisfy the differential equation as well as possible.
Finitely generated moduleIn mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type. Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.
Finite morphismIn algebraic geometry, a finite morphism between two affine varieties is a dense regular map which induces isomorphic inclusion between their coordinate rings, such that is integral over . This definition can be extended to the quasi-projective varieties, such that a regular map between quasiprojective varieties is finite if any point like has an affine neighbourhood V such that is affine and is a finite map (in view of the previous definition, because it is between affine varieties).
00 (zero) is a number representing an empty quantity. As a number, 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and other algebraic structures. In place-value notation such as decimal, 0 also serves as a numerical digit to indicate that that position's power of 10 is not multiplied by anything or added to the resulting number. This concept appears to have been difficult to discover. Common names for the number 0 in English are zero, nought, naught (nɔːt), nil.
ForceIn physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. It is measured in the SI unit of newton (N) and often represented by the symbol F.
Centripetal forceA centripetal force (from Latin centrum, "center" and petere, "to seek") is a force that makes a body follow a curved path. The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In the theory of Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits.
Central forceIn classical mechanics, a central force on an object is a force that is directed towards or away from a point called center of force. where is the force, F is a vector valued force function, F is a scalar valued force function, r is the position vector, ||r|| is its length, and is the corresponding unit vector. Not all central force fields are conservative or spherically symmetric. However, a central force is conservative if and only if it is spherically symmetric or rotationally invariant.
Manning formulaThe Manning formula or Manning's equation is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, i.e., open channel flow. However, this equation is also used for calculation of flow variables in case of flow in partially full conduits, as they also possess a free surface like that of open channel flow. All flow in so-called open channels is driven by gravity.
