Calculus Definitions > What is Propositional Calculus? Propositional calculus (sometimes called sentential calculus) is a simplified version of symbolic logic; It is a way to analyze truth relationships between compound propositions and their individual parts (Kahn, 2007). The calculus involves…

Calculus Definitions > An open set contains its boundary; it is a generalization of an open interval. A closed set does not contain its boundary and is a generalization of a closed interval. In topology, a closed set is defined…

Calculus Problem Solving > Surface Area Calculus The surface area generated by a volume of revolution (for example, the surface of a sphere) can be approximated with calculus. One technique is to find a curve, that when rotated around an…

Analytic Geometry > A quadric surface is a 3D extension of a conic (ellipsis, hyperbola, or parabola). In 2D space, they are defined by quadratic equations in 2D space [1]. Quadric refers to the degree of the equation describing the…

Types of Functions > For many continuous random variables, we can define a probability density function (PDF) to find probabilities of the variable falling within a range, say a and b. This probability is denoted by P (a < X…

Types of Functions > What is a Likelihood Function? Many probability distributions have unknown parameters; We estimate these unknowns using sample data. The Likelihood function gives us an idea of how well the data summarizes these parameters. The “parameters” here…

Types of Functions > The iterated logarithm functionlog * n (“log star of n”) is defined as the smallest natural number k for which log(i) ≤ 1. The function is not defined for n < 1. Formally, it is defined…

Analytic Geometry > A hyperbola is an open curve with two opposite, mirror-image parabolas. More formally, it is a collection of points in the plane where the absolute value of the difference of the distances from a point on the…

Non-Newtonian Calculus > Geometric calculus (also called exponential calculus) is an extension of geometric algebra to include differentiation and integration [1]. Basic Problem of Geometric Calculus and Fundamental Concepts The basic problem of geometric calculus is as follows: “Suppose that…

Calculus Definitions > A nullcline is a point where a vector field changes direction [1]. The name means zero (null) slope (cline). Nullcline in Differential Equations In an autonomous system of two differential equations They can be defined as [2,…