# Calculus Glossary

## What are Second-Order Differential Equations?

Second-order differential equations involve the second derivative of a function and are used to model various phenomena in mathematics, physics, and engineering. Learn about common solution methods.

## What is a Bifurcation Point?

Bifurcation points are points in the parameter space of a dynamical system where the system’s behavior changes qualitatively. Discover their importance in understanding stability and transitions in nonlinear systems.

## What is an Integration Factor?

An integration factor is a technique used to solve first-order linear ordinary differential equations by transforming the equation into an exact differential equation. Learn about the process and its applications.

## What is the Existence and Uniqueness Theorem?

The Existence and Uniqueness Theorem establishes conditions for the existence of a unique solution to an initial value problem in ordinary differential equations. Learn about its importance in the study of ODEs.

## What is the Bolzano-Weierstrass Theorem?

The Bolzano-Weierstrass Theorem states that every bounded sequence of real numbers has a convergent subsequence. This fundamental result in real analysis plays a crucial role in calculus.

## What is the First Derivative Test?

The First Derivative Test is a method in calculus for determining the nature of a critical point of a continuous function, helping to identify local maximums, local minimums, or neither.

## What is the Second Derivative Test?

The Second Derivative Test is a method in calculus for determining the nature of a critical point of a function by analyzing the value of the second derivative at the critical point.

## What is a Surface Integral?

Surface integrals extend the concept of line integrals to two-dimensional surfaces, calculating the accumulation of a scalar or vector quantity over a surface in three-dimensional space.

## What is a Line Integral?

Line integrals are a fundamental concept in multivariable calculus, used to calculate the accumulation of a scalar or vector quantity along a curve and find applications in various fields.

## What is an Orthogonal Trajectory?

An orthogonal trajectory is a family of curves that intersect another family of curves at right angles at every point of intersection, with applications in physics, geometry, and engineering.