Differential equations are mathematical equations that involve functions and their derivatives, representing physical phenomena and changes in various fields such as physics, engineering, and economics. They are essential for modeling and solving problems where quantities change continuously, providing insights into the behavior and dynamics of complex systems.
Stability analysis is a mathematical technique used to determine the ability of a system to return to equilibrium after a disturbance. It is crucial in various fields such as engineering, economics, and control theory to ensure system reliability and performance under changing conditions.
A family of curves is a set of curves that are related through a common parameter, allowing for the exploration of how changes in this parameter affect the shape and position of the curves. This concept is widely used in calculus and differential equations to analyze and visualize solutions that depend on initial conditions or parameters.