DerivativeIn mathematics, the derivative shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Middle classThe middle class refers to a class of people in the middle of a social hierarchy, often defined by occupation, income, education, or social status. The term has historically been associated with modernity, capitalism and political debate. Common definitions for the middle class range from the middle fifth of individuals on a nation's income ladder, to everyone but the poorest and wealthiest 20%. Theories like "Paradox of Interest" use decile groups and wealth distribution data to determine the size and wealth share of the middle class.
Upper classUpper class in modern societies is the social class composed of people who hold the highest social status, usually are the wealthiest members of class society, and wield the greatest political power. According to this view, the upper class is generally distinguished by immense wealth which is passed on from generation to generation. Prior to the 20th century, the emphasis was on aristocracy, which emphasized generations of inherited noble status, not just recent wealth.
Partial derivativeIn mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function with respect to the variable is variously denoted by It can be thought of as the rate of change of the function in the -direction.
Jacobi elliptic functionsIn mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for .
Differentiation rulesThis is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Unless otherwise stated, all functions are functions of real numbers (R) that return real values; although more generally, the formulae below apply wherever they are well defined — including the case of complex numbers (C). For any value of , where , if is the constant function given by , then . Let and . By the definition of the derivative, This shows that the derivative of any constant function is 0.
Many-minds interpretationThe many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. The concept was first introduced in 1970 by H. Dieter Zeh as a variant of the Hugh Everett interpretation in connection with quantum decoherence, and later (in 1981) explicitly called a many or multi-consciousness interpretation. The name many-minds interpretation was first used by David Albert and Barry Loewer in 1988.
Algebraic curveIn mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation h(x, y, t) = 0 can be restricted to the affine algebraic plane curve of equation h(x, y, 1) = 0.
SpeedIn everyday use and in kinematics, the speed (commonly referred to as v) of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.
Hyperbolic functionsIn mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola. Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t) respectively, the derivatives of sinh(t) and cosh(t) are cosh(t) and +sinh(t) respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry.
Interval (mathematics)In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
