Types of Functions > What is a Bump Function? A bump function (sometimes called a test function) is, perhaps not surprisingly, a function with a “bump.” A simple example is the real-valued function The function is defined on the open…

## Linear Form: Definition, Examples

Calculus Definitions > The term “linear form” has a few different meanings in math and calculus. The exact definition depends on where you are using it: Algebra & Equations for Lines Differential Equations Other Areas of Math 1. Linear Form…

## Draw Graph of Derivative

Calculus Problem solving > There are two types of problems that might ask you to draw the graph of a derivative: given a function, or not given a function. You can use the same procedure for both types of problems.…

## Stochastic Function: Definition, Examples

Types of Functions > What is a Stochastic Function? A stochastic function is a function with an uncertain input [1]. One or more of the function’s parameters has a term with statistical noise. A stochastic function can also be described…

## Abel’s Inequality: Definition & Proof

Calculus Definitions > Abel’s Inequality, named after 19th Century Norwegian mathematician Niels Abel, is an estimate for the sum of products of two numbers. Let’s ak and bk are two sets of numbers. First, let’s look at the numbers bk…

## Malliavin Calculus: An Overview

Calculus Definitions > What is Malliavin Calculus? Malliavin calculus, also called the stochastic calculus of variations, extends calculus of variations from deterministic functions to stochastic (random) processes. More specifically, it differentiates random variables defined on a Gaussian probability space (usually…

## Tangent Vector (Velocity Vector)

Calculus Definitions > A tangent vector T (also called a velocity vector) shows the direction of motion. It points in the direction of the tangent line and has its base at the point of tangency on the curve rather than…

## Algebraic Limit Theorem: Definition, Examples

Calculus Definitions > The algebraic limit theorem shows us that sequences behave in an orderly fashion when subjected to mathematical operations. Formally stated, the algebraic limit theorem is [1]: If a = lim an and b = lim bn, then…

## How to Find the Sum of a Series

Calculus Problem Solving > The sum of a series is the total the list of numbers add up to. If the sum of a series exists, it will be a single number, like 0, 1, or 99. In most cases,…

## Infinite Product

Calculus Definitions > The definition of an infinite product is very similar to the definition of an infinite sum. Instead of adding an infinite number of terms, you’re multiplying. For example, 1·2·3·,…,∞. More formally, let {xn} represent a numerical series.…