# Calculus Glossary

## What is the Mean Value Theorem?

The Mean Value Theorem is a foundational theorem in calculus that relates the average rate of change of a function to its instantaneous rate of change at a specific point.

## What is Curl?

Curl is a vector operator that measures the rotation of a vector field around a point, used in fluid dynamics, electromagnetism, and other fields involving vector fields.

## What are Runge-Kutta Methods?

Runge-Kutta methods are numerical techniques for solving initial value problems in ordinary differential equations. Learn about the popular fourth-order Runge-Kutta method and its applications.

## What is the Comparison Test?

The Comparison Test is a method in calculus for determining the convergence or divergence of an infinite series by comparing its terms to those of another series with known convergence properties. Learn about its application and use.

## What is the Root Test?

The Root Test is a method in calculus for determining the convergence or divergence of an infinite series by examining the limit of the nth root of the absolute value of the terms. Learn about its application and use.

## What is the Ratio Test?

The Ratio Test is a method in calculus for determining the convergence or divergence of an infinite series by examining the limit of the ratio of consecutive terms.

## What is a Directional Derivative?

A directional derivative is a measure of the rate of change of a function in a specific direction, calculated as the dot product of the gradient vector and the unit vector in the desired direction.

## What are Inhomogeneous Differential Equations?

Inhomogeneous differential equations are a type of partial or ordinary differential equation with a non-zero term, used to model various phenomena in physics, engineering, and mathematics, with several solution techniques available.

## What is Green’s Function?

Green’s function is a mathematical tool used to solve inhomogeneous partial differential equations and boundary value problems, with applications in various fields, including physics, engineering, and applied mathematics.

## What is a Scalar Field?

A scalar field is a function that assigns a scalar value to each point in space, representing quantities with magnitude but not direction and playing an important role in vector calculus, physics, engineering, and mathematical analysis.