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.

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.

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.

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.

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.

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.

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.

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.

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.

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.