Power seriesIn mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, c (the center of the series) is equal to zero, for instance when considering a Maclaurin series.
Deflection (engineering)In structural engineering, deflection is the degree to which a part of a structural element is displaced under a load (because it deforms). It may refer to an angle or a distance. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations.
T-beamA T-beam (or tee beam), used in construction, is a load-bearing structure of reinforced concrete, wood or metal, with a -shaped cross section. The top of the -shaped cross section serves as a flange or compression member in resisting compressive stresses. The web (vertical section) of the beam below the compression flange serves to resist shear stress. When used for highway bridges the beam incorporates reinforcing bars in the bottom of the beam to resist the tensile stresses which occur during bending.
Madhava seriesIn mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century Kerala by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. Using modern notation, these series are: All three series were later independently discovered in 17th century Europe.
Taylor's theoremIn calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation.
Fluid solutionIn general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid. In astrophysics, fluid solutions are often employed as stellar models. (It might help to think of a perfect gas as a special case of a perfect fluid.) In cosmology, fluid solutions are often used as cosmological models.
Solid mechanicsSolid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics and chemistry such as materials science.
BucklingIn structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column.
Dust solutionIn general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure. Dust solutions are an important special case of fluid solutions in general relativity. A pressureless perfect fluid can be interpreted as a model of a configuration of dust particles that locally move in concert and interact with each other only gravitationally, from which the name is derived.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
