The method of undetermined coefficients is a technique for solving non-homogeneous linear differential equations with constant coefficients, applicable when the non-homogeneous term is a simple function. It involves assuming a particular solution with undetermined coefficients, then solving for them by substituting the assumed solution into the differential equation.
The polar coordinate system represents points by their distance from the origin and angle with the reference direction. Discover its usefulness in various problems and calculus applications.
Partial fraction decomposition is a calculus technique for breaking down a complex rational function into simpler rational functions. Discover its uses and methods for performing decomposition.
L’Hopital’s Rule is a calculus method for finding the limit of a quotient of two functions when both approach zero or infinity. Learn how to apply L’Hopital’s Rule to simplify and evaluate limits.
Asymptotes are lines that a function’s graph approaches but never reaches. Learn about vertical, horizontal, and oblique asymptotes and how they help analyze a function’s behavior.
An inflection point is a point on the graph of a function where the concavity changes, indicating a change in the overall behavior of the function. Discover how to find and analyze inflection points.
A critical point is a point on the graph of a function where the derivative is zero or undefined, often corresponding to local extrema or points of inflection. Learn how to identify and analyze critical points.
A bounded function is a function whose values lie within a specific range, having an upper and lower bound. Learn about its role in calculus, convergence, and continuity.
A divergent series is a mathematical series that does not converge to a finite limit as the number of terms goes to infinity. Discover its characteristics and applications.
A convergent series is a mathematical series whose terms approach a finite limit as the number of terms goes to infinity. Learn about its role in calculus and tests for convergence.