AP Calculus AB, unit: Differential Equations. Conceptual understanding and key rules for this unit, explained in plain language alongside the formula. Front: a concept or short problem cue. Back: the explanation, rule, or answer.
13 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a differential equation?
- An equation relating a function to its derivatives
- What is a slope field?
- A graphical representation showing the slope of solutions to a differential equation at various points
- What is separation of variables used for?
- Solving a differential equation by isolating each variable on opposite sides before integrating
- What is a general solution to a differential equation?
- A family of solutions including an arbitrary constant
- What is a particular solution to a differential equation?
- A specific solution satisfying a given initial condition
- What is an initial condition, in a differential equation problem?
- A known value of the function at a specific point, used to find a particular solution
- What is exponential growth modeled by?
- A differential equation where the rate of change is proportional to the current amount
- What is the general solution to dy/dx = ky?
- y = C times e^(kt), where C is determined by the initial condition
- What does a positive value of k represent in exponential growth models?
- Growth, where the quantity increases over time
- What does a negative value of k represent in exponential models?
- Decay, where the quantity decreases over time
- What is Euler's Method used for?
- Numerically approximating solutions to a differential equation using small linear steps
- What is logistic growth?
- A growth model where the rate of change slows as the quantity approaches a carrying capacity
- What does verifying a solution to a differential equation involve?
- Substituting the proposed function and its derivatives back into the equation to confirm it holds
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