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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
t. e. In mathematics, an ordinary differential equation ( ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown (s) consists of one (or more) function (s) and involves the derivatives of those functions. [ 1] The term "ordinary" is used in contrast with partial differential equations ...
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. [ 1] Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, called a parametric curve and parametric surface, respectively.
Algebraic equation. In mathematics, an algebraic equation or polynomial equation is an equation of the form , where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, is an algebraic equation with integer coefficients and. is a multivariate polynomial equation over the rationals.
Debye–Hückel theory. The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas . [ 1] It is a linearized Poisson–Boltzmann model, which assumes an extremely simplified model of electrolyte solution but nevertheless gave ...
where r 2 and r 1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant. Euler's equations for rigid body dynamics [ edit ]
To state this formally, in general an equation of motion M is a function of the position r of the object, its velocity (the first time derivative of r, v = dr dt ), and its acceleration (the second derivative of r, a = d2r dt2 ), and time t. Euclidean vectors in 3D are denoted throughout in bold.
The graph of a degree 1 polynomial (or linear function) f(x) = a0 + a1x, where a1 ≠ 0, is an oblique line with y-intercept a0 and slope a1 . The graph of a degree 2 polynomial. f(x) = a0 + a1x + a2x2, where a2 ≠ 0. is a parabola . The graph of a degree 3 polynomial. f(x) = a0 + a1x + a2x2 + a3x3, where a3 ≠ 0.