Calculus Definitions > The marginal cost (MC) is the change in total cost when the quantity produced changes by one unit. In other words, it’s the extra cost associate with producing one item. More formally, the marginal cost (MC) function…

Calculus Derivatives > The fourth derivative (also called a jounce or snap) is when you take the derivative of a function four times. In other words: Find the first derivative, then Find the second derivative, then Find the third derivative,…

Calculus Curves > The lituus is a transcendental curve that can be graphed with the polar equation r = k/√θ [1] or, equivalently, r2 = a2/θ. The inverse of the lituus is Fermat’s spiral – a type of Archimedean spiral…

Calculus Curves > The alysoid (from the Greek Alusion, meaning “little chain”) is a transcendental curve first studied by Italian mathematician Ernesto Cesàro in 1886. The curve can be formed by a flexible chain of an infinite number of links,…

Integral Calculus > Contents: Probability Integral Integral of the normal distribution Integral Transform Probability Integral The probability integral (also called the Gaussian Integral) is the integral of the one-dimensional Gaussian (or normal distribution) over (-∞,∞). It can be calculated by…

Calculus Definitions > An intermediate variable serves as a causal link between other variables. It is acted on by the independent variable and then acts itself on the dependent variable to create change. For example, suppose you wanted to look…

Types of Functions > The regularized incomplete beta function (also called the regularized beta function) is widely used in statistics and some areas of physics as the cumulative distribution function of the beta distribution [1]. It represent the CDF for…

Calculus Curves > A catacaustic is a curve formed when light is reflected off of another curve, forming an envelope of reflected rays. If light is refracted instead, it is diacaustic. For example, the nephroid is the catacaustic of the…

Derivatives > The convective derivative, also called a Lagrangian derivative, is commonly used in classical and fluid mechanics and is also found in a wide variety of other sciences such as also astrophysics and cosmology. It is a derivative taken…

Analytic Geometry > Trilinear coordinates, introduced by Möbius in 1827, is a way to identify a point in a plane with respect to a triangle. The coordinates are defined by measuring signed distances from a triangle’s sides. Basically, it is…